For Class 8, 9 & 10
Master the basics - and everything after gets easier
Concept-first questions with clear model answers in Physics, Chemistry, Maths and Biology, all NCERT-aligned. Start early, build the habit, and walk into your boards, NEET and JEE already ahead.
Interactive lessons
learn by playingDrag, slide and build - watch each concept come alive, then reveal the answer.
200 interactive lessons
Ohm's law
Class 10 Physics
Slide V & R, watch the bulb glow
Open →pH scale
Class 10 Chemistry
Slide across acids and bases
Open →Atomic number and mass number
Class 9 Chemistry
Add protons & neutrons, build shells
Open →Laws of reflection
Class 8 Physics
Change the angle, watch it bounce
Open →Volume of a sphere
Class 9 Maths
Grow the radius, see the volume
Open →Area of a trapezium
Class 8 Maths
Drag the sides, read the area
Open →Power of a lens
Class 10 Physics
Move the object, trace the rays
Open →Food chain and energy flow
Class 10 Biology
Follow the energy as it flows
Open →Speed
Class 8 Physics
Slide distance & time, watch the speed
Open →Density
Class 9 Physics
Pack mass into volume, float or sink
Open →Work done
Class 9 Physics
Push harder or farther, watch work grow
Open →Kinetic energy
Class 9 Physics
Speed it up - energy grows with the square
Open →Power of a lens
Class 10 Physics
Shorten the focal length, boost the power
Open →Mole concept
Class 9 Chemistry
Weigh out grams, count the moles
Open →Avogadro's number
Class 9 Chemistry
Add moles, count the particles
Open →Microscope magnification
Class 8 Biology
Grow the image, read the magnification
Open →Population density
Class 10 Biology
Add individuals, shrink the land, see crowding
Open →Simple interest
Class 8 Maths
Slide money, rate & time, watch interest
Open →Pythagoras theorem
Class 9 Maths
Stretch the two sides, get the hypotenuse
Open →Probability of an event
Class 10 Maths
Change the outcomes, watch the odds
Open →Newton's second law
Class 9 Physics
Push a mass, pick an acceleration
Open →Momentum
Class 9 Physics
Slide mass & velocity, build momentum
Open →Pressure
Class 8 Physics
Shrink the area, feel the pressure rise
Open →Weight
Class 9 Physics
Change the planet's gravity, watch your weight
Open →Refractive index
Class 10 Physics
Slow light in the medium, raise the index
Open →Resistors in series
Class 10 Physics
Add two resistors in a line
Open →Mass percentage of a solution
Class 9 Chemistry
Dissolve solute, read the strength
Open →Concentration of a solution
Class 9 Chemistry
Pack solute into less liquid
Open →Population change
Class 10 Biology
Balance births against deaths
Open →Compound microscope
Class 8 Biology
Combine eyepiece & objective lenses
Open →Area of a circle
Class 8 Maths
Grow the radius, watch the area square
Open →Volume of a cuboid
Class 8 Maths
Stretch length, breadth & height
Open →Electronic configuration and valency
Class 9 Chemistry
Slide the atomic number, build the atom
Open →Homologous series (alkanes)
Class 10 Chemistry
Add carbons, name the compound
Open →Mass number
Class 9 Chemistry
Add protons & neutrons, get the mass number
Open →Power
Class 9 Physics
More work in less time = more power
Open →Potential energy
Class 9 Physics
Lift a mass higher, store energy
Open →Wave speed
Class 9 Physics
Tune frequency & wavelength, set the speed
Open →Electric current
Class 10 Physics
Push charge per second, get the current
Open →Percentage
Class 8 Maths
Compare part to whole as a %
Open →Electron dot structure
Class 9 Chemistry
Draw valence electrons as dots
Open →Acceleration
Class 9 Physics
Speed up over time, find acceleration
Open →Distance, speed and time
Class 8 Physics
Set speed & time, cover the distance
Open →Frequency and time period
Class 9 Physics
Shorten the period, raise the frequency
Open →Heating effect of current
Class 10 Physics
Raise the current, watch heating soar
Open →Area of a triangle
Class 8 Maths
Set base & height, halve the rectangle
Open →Area of a rectangle
Class 8 Maths
Set length & breadth, fill the area
Open →Mean (average)
Class 9 Maths
Share the total equally across items
Open →Discount
Class 8 Maths
Slide price & % off, see the saving
Open →Heart rate
Class 10 Biology
Set heart rate & time, count the beats
Open →Resistors in parallel
Class 10 Physics
Wire two resistors side by side
Open →Electric charge
Class 10 Physics
Flow current over time, collect charge
Open →Electrical energy and units
Class 10 Physics
Run appliances, add up the units
Open →Kelvin temperature scale
Class 9 Chemistry
Slide Celsius, read the Kelvin
Open →Moles from number of particles
Class 9 Chemistry
Divide particles by Avogadro's number
Open →Ten percent law
Class 10 Biology
See 10% of energy reach the next level
Open →Area of a square
Class 8 Maths
Grow the side, square the area
Open →Volume of a cube
Class 8 Maths
Grow the edge, cube the volume
Open →Circumference of a circle
Class 8 Maths
Grow the radius, roll out the rim
Open →Surface area of a cube
Class 9 Maths
Grow the edge, cover six faces
Open →Potential difference
Class 10 Physics
Share work across charge, get volts
Open →Resistance from Ohm's law
Class 10 Physics
Divide voltage by current, get resistance
Open →Echo and SONAR
Class 9 Physics
Time the echo, find the distance
Open →Mass from moles
Class 9 Chemistry
Multiply moles by molar mass
Open →Breathing rate
Class 10 Biology
Set breathing rate & time
Open →Volume of a cylinder
Class 10 Maths
Set radius & height, fill the can
Open →Compound interest
Class 8 Maths
Compound money over years
Open →Profit and loss percentage
Class 8 Maths
Set cost & selling price, see profit %
Open →Perimeter of a rectangle
Class 8 Maths
Set length & breadth, walk the border
Open →Surface area of a sphere
Class 10 Maths
Grow the radius, wrap the ball
Open →Time period
Class 9 Physics
Raise the frequency, shrink the period
Open →Relative velocity
Class 9 Physics
Two objects approach - add their speeds
Open →Average velocity
Class 9 Physics
Average the start and end speeds
Open →Equations of motion (v = u + at)
Class 9 Physics
Accelerate from u for a time t
Open →Kelvin to Celsius
Class 9 Chemistry
Slide Kelvin, read the Celsius
Open →Population growth rate
Class 10 Biology
Balance births vs deaths per population
Open →Perimeter of a square
Class 8 Maths
Grow the side, walk four edges
Open →Perimeter of a triangle
Class 8 Maths
Add the three sides
Open →Area of a parallelogram
Class 8 Maths
Set base & height, slide the shape
Open →Area of a rhombus
Class 8 Maths
Set the two diagonals
Open →Equations of motion (distance)
Class 9 Physics
Start, accelerate, cover ground
Open →Joule's law of heating
Class 10 Physics
Raise current, resistance or time
Open →Electric power (P = VI)
Class 10 Physics
Multiply voltage by current
Open →Average atomic mass of isotopes
Class 9 Chemistry
Mix two isotopes by abundance
Open →Seed germination percentage
Class 9 Biology
Count sprouted seeds out of the total
Open →Volume of a cone
Class 9 Maths
Set radius & height, fill the cone
Open →Surface area of a cylinder
Class 9 Maths
Wrap the side and both ends
Open →Surface area of a cuboid
Class 9 Maths
Cover all six rectangular faces
Open →nth term of an AP
Class 10 Maths
Step from the first term by d
Open →Sum of an AP
Class 10 Maths
Add up the first n terms
Open →Focal length of a mirror
Class 10 Physics
Halve the radius to find the focus
Open →Speed of light in a medium
Class 10 Physics
Raise the index, slow the light
Open →Percentage purity
Class 9 Chemistry
Weigh the pure part of a sample
Open →Slope of a line
Class 10 Maths
Rise over run gives the steepness
Open →Percentage change
Class 8 Maths
Compare a new value to the old
Open →Volume of a hemisphere
Class 9 Maths
Grow the radius of half a ball
Open →Area of a sector
Class 10 Maths
Cut a slice of angle from a circle
Open →Length of an arc
Class 10 Maths
Measure the curved edge of a slice
Open →Slant height of a cone
Class 9 Maths
Combine radius & height for the slant
Open →Unit conversion (km/h to m/s)
Class 9 Physics
Convert km/h into m/s
Open →Equations of motion (v^2 = u^2 + 2as)
Class 9 Physics
Accelerate over a distance, find v
Open →Impulse
Class 9 Physics
Hit harder or longer, change momentum
Open →Wavelength
Class 9 Physics
Speed over frequency gives wavelength
Open →Oscillations
Class 9 Physics
Vibrate at a frequency for a time
Open →Cost of electricity
Class 10 Physics
Units times rate gives the bill
Open →Number of neutrons
Class 9 Chemistry
Take protons away from the mass number
Open →Curved surface area of a cone
Class 9 Maths
Wrap the slanted side of a cone
Open →Total surface area of a cone
Class 9 Maths
Add the base circle to the cone's side
Open →Curved surface area of a hemisphere
Class 9 Maths
Cover the dome of a hemisphere
Open →Diagonal of a square
Class 9 Maths
Cross a square corner to corner
Open →Unit conversion (m/s to km/h)
Class 9 Physics
Convert m/s into km/h
Open →Distance from velocities
Class 9 Physics
From two speeds, find the distance
Open →Diagonal of a rectangle
Class 9 Maths
Cross a rectangle corner to corner
Open →Diagonal of a cuboid
Class 9 Maths
The longest rod that fits in a box
Open →Area by Heron's formula
Class 9 Maths
Area from just the three sides
Open →Interior angle sum of a polygon
Class 8 Maths
Add up a polygon's inside angles
Open →Exterior angle of a regular polygon
Class 8 Maths
Share 360 among a polygon's corners
Open →Number of diagonals of a polygon
Class 8 Maths
Count the diagonals of a polygon
Open →Discriminant
Class 10 Maths
Test how many roots a quadratic has
Open →Sum of roots
Class 10 Maths
Sum of a quadratic's roots
Open →Punnett square (monohybrid cross)
Class 10 Biology
Cross two parents, predict the offspring
Open →Balancing chemical equations
Class 10 Chemistry
Slide coefficients until atoms balance
Open →Writing chemical formulae (valency)
Class 9 Chemistry
Criss-cross valencies into a formula
Open →Current from power
Class 10 Physics
Divide power by voltage for current
Open →Power (P = V^2 / R)
Class 10 Physics
Voltage squared over resistance
Open →Sine ratio
Class 10 Maths
Opposite over hypotenuse
Open →Cosine ratio
Class 10 Maths
Adjacent over hypotenuse
Open →Tangent ratio
Class 10 Maths
Opposite over adjacent
Open →Area of an equilateral triangle
Class 9 Maths
Area of an equilateral triangle
Open →Curved surface area of a cylinder
Class 9 Maths
Wrap only the curved side
Open →Loss percentage
Class 8 Maths
Sell below cost, find the loss %
Open →Amount with simple interest
Class 8 Maths
Principal plus its simple interest
Open →Distance formula
Class 10 Maths
Straight distance between two points
Open →States of matter
Class 9 Chemistry
Heat particles solid → liquid → gas
Open →Parts of a plant cell
Class 8 Biology
Tap a cell part to see its job
Open →Diagonal of a cube
Class 9 Maths
Longest diagonal through a cube
Open →Total surface area of a hemisphere
Class 9 Maths
Dome plus its flat circle
Open →Sum of first n natural numbers
Class 10 Maths
Add 1 + 2 + ... + n instantly
Open →Range of data
Class 9 Maths
Spread from smallest to largest
Open →Class mark
Class 9 Maths
Midpoint of a class interval
Open →Selling price from profit percent
Class 8 Maths
Mark up cost by a profit %
Open →Perimeter of a sector
Class 10 Maths
Two radii plus the curved arc
Open →Circumference from diameter
Class 8 Maths
Circumference straight from diameter
Open →Power (P = F x v)
Class 9 Physics
Force times velocity gives power
Open →Percentage of a number
Class 8 Maths
Find a percentage of a number
Open →Series and parallel circuits
Class 10 Physics
Break a bulb in series vs parallel
Open →Symbols of elements
Class 9 Chemistry
Match each element to its symbol
Open →Free fall (velocity)
Class 9 Physics
Drop from a height, hit this speed
Open →Free fall (time)
Class 9 Physics
How long a drop takes
Open →Free fall (distance)
Class 9 Physics
Distance fallen in a given time
Open →Complement of an event
Class 10 Maths
Chance an event does NOT happen
Open →Product of roots
Class 10 Maths
Product of a quadratic's roots
Open →Exterior angle theorem
Class 9 Maths
Exterior angle = sum of remote interiors
Open →Complementary angles
Class 10 Maths
What adds to 90 degrees
Open →Supplementary angles
Class 9 Maths
What adds to 180 degrees
Open →Perimeter of a semicircle
Class 10 Maths
Curved half plus the diameter
Open →Area of a semicircle
Class 10 Maths
Half the area of a circle
Open →Turning effect (moments)
Class 9 Physics
Balance the see-saw with moments
Open →Reflex arc
Class 10 Biology
Step through a reflex, stimulus to action
Open →Buoyant force (upthrust)
Class 9 Physics
Displace liquid, feel the upthrust
Open →Relative density
Class 9 Physics
Compare a density to water's
Open →Power in lifting a load
Class 9 Physics
Lift a load, faster needs more power
Open →Cosecant ratio
Class 10 Maths
Hypotenuse over opposite
Open →Secant ratio
Class 10 Maths
Hypotenuse over adjacent
Open →Cotangent ratio
Class 10 Maths
Adjacent over opposite
Open →Height from angle of elevation
Class 10 Maths
Height from an angle of elevation
Open →Area of a quadrant
Class 10 Maths
A quarter of a circle's area
Open →Interior angle of a regular polygon
Class 8 Maths
One inside angle of a regular polygon
Open →Sum of first n odd numbers
Class 10 Maths
Add the first n odd numbers
Open →Sum of first n even numbers
Class 10 Maths
Add the first n even numbers
Open →Quadratic formula (a root)
Class 10 Maths
Larger root of a quadratic
Open →LCM from HCF
Class 10 Maths
LCM from the product and HCF
Open →Depreciation
Class 8 Maths
Value drops by a % each year
Open →Cost price from selling price
Class 8 Maths
Work back to the cost price
Open →Downstream speed
Class 8 Maths
Row with the current
Open →Upstream speed
Class 8 Maths
Row against the current
Open →Average speed for a round trip
Class 8 Maths
Average speed there and back
Open →Sales tax / GST
Class 8 Maths
Tax added on a price
Open →Area of a ring (annulus)
Class 10 Maths
Area of a ring between two circles
Open →Edge of a cube from volume
Class 9 Maths
Edge back from the volume
Open →Radius from area
Class 10 Maths
Radius back from a circle's area
Open →Side from area of a square
Class 8 Maths
Side back from a square's area
Open →Height of a triangle from area
Class 9 Maths
Height back from area and base
Open →Rate from simple interest
Class 8 Maths
Rate back from the interest
Open →Time from simple interest
Class 8 Maths
Time back from the interest
Open →Principal from simple interest
Class 8 Maths
Principal back from the interest
Open →Mean proportional
Class 10 Maths
Geometric mean of two numbers
Open →Fourth proportional
Class 8 Maths
Complete the proportion a : b = c : ?
Open →Marked price from selling price
Class 8 Maths
Marked price back from the sale price
Open →Chambers of the human heart
Class 10 Biology
Tap a heart chamber to see its job
Open →Equation of a line (y = mx + c)
Class 9 Maths
Read y off a straight line
Open →Average term of an AP
Class 10 Maths
Average of first and last term
Open →Number of terms in an AP
Class 10 Maths
How many terms in an AP
Open →Midpoint of two points
Class 10 Maths
x-coordinate of a midpoint
Open →Empirical mode
Class 10 Maths
Estimate the mode from mean & median
Open →Length of a shadow
Class 10 Maths
Shadow from height and sun angle
Open →Train crossing a pole
Class 8 Maths
Speed to cross a pole
Open →Time and work
Class 8 Maths
More workers, fewer days
Open →Dividing in a ratio
Class 8 Maths
Split a total in a ratio
Open →Unitary method
Class 8 Maths
Cost of a single item
Open →Your progress — Foundation - Class 8 to 10
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Showing 18 questions for Class 8. Tap a card to reveal the answer.
MathematicsMensurationmediumFind the area of a trapezium whose parallel sides are 12 cm and 8 cm and whose height is 5 cm.
Reveal answer ↓
What it is
A trapezium's area is the average of its two parallel sides times the height.
Area = ½ (a + b) h = ½ (8 + 12) × 5 = 50 cm²
Answer
Area of a trapezium = (1/2) x (sum of parallel sides) x height = (1/2) x (12 + 8) x 5 = (1/2) x 20 x 5 = 50 square cm.
Area = (1/2)(a + b) x h
- •Area = (1/2)(a + b) h
- •= (1/2)(12 + 8)(5)
- •= 50 cm^2
Why learn this
It measures real shapes - fields, plots and cross-sections that are not perfect rectangles.
💡 Memory trick
Half the sum of the parallel sides, times the height: (1/2)(a + b) h.
MathematicsMensurationeasyFind the area of a circle of radius 7 units (take pi = 3.14159). Slide the radius to explore.
Reveal answer ↓
What it is
The area of a circle grows with the square of its radius.
Answer
Area = pi x r^2 = 3.14159 x 7^2 = 3.14159 x 49 = 153.94 square units. Because the radius is squared, doubling it makes the area four times as large.
A = pi x r^2
- •Area = pi x r^2
- •Unit: square units
- •Double the radius -> four times the area
Why learn this
It sizes anything round - plots, pipes, plates and wheels.
💡 Memory trick
Area = pi x r^2. Double r -> four times the area.
MathematicsMensurationeasyFind the volume of a cuboid 3 x 4 x 5 units. Slide the dimensions to explore.
Reveal answer ↓
What it is
The volume of a cuboid is the product of its length, breadth and height.
Answer
Volume = length x breadth x height = 3 x 4 x 5 = 60 cubic units. Increasing any one of the three dimensions increases the volume in proportion.
V = l x b x h
- •Volume = l x b x h
- •Unit: cubic units
- •Change any dimension -> volume scales with it
Why learn this
It's how we measure the space in boxes, rooms and tanks.
💡 Memory trick
Volume = l x b x h. All three dimensions multiply.
MathematicsMensurationeasyFind the area of a triangle with base 10 and height 8 units. Slide to explore.
Reveal answer ↓
What it is
The area of a triangle is half the product of its base and height.
Answer
Area = 1/2 x base x height = 1/2 x 10 x 8 = 40 square units. A triangle covers exactly half of a rectangle with the same base and height, which is where the 1/2 comes from.
A = 1/2 x base x height
- •Area = 1/2 x base x height
- •Unit: square units
- •Half of the matching rectangle
Why learn this
Triangles tile every roof, ramp and truss we build.
💡 Memory trick
Area = 1/2 x base x height - half of the matching rectangle.
MathematicsMensurationeasyFind the area of a rectangle 5 units long and 4 units wide. Slide to explore.
Reveal answer ↓
What it is
The area of a rectangle is its length multiplied by its breadth.
Answer
Area = length x breadth = 5 x 4 = 20 square units. If the length and breadth are equal, the rectangle is a square and the area becomes side x side.
A = length x breadth
- •Area = length x breadth
- •Unit: square units
- •Square is the special case length = breadth
Why learn this
It's the first area formula, used for floors, walls and screens.
💡 Memory trick
Area = length x breadth. Square is the case length = breadth.
MathematicsMensurationeasyFind the area of a square of side 6 units. Slide the side to explore.
Reveal answer ↓
What it is
The area of a square is the length of its side multiplied by itself.
Answer
Area = side x side = 6 x 6 = 36 square units. Because the side is squared, doubling it to 12 makes the area 144 - four times as large.
A = side^2
- •Area = side^2
- •Unit: square units
- •Double the side -> four times the area
Why learn this
It's the simplest area formula, used for tiles, boards and plots.
💡 Memory trick
Area = side x side = side^2. Double the side -> four times the area.
MathematicsMensurationeasyFind the volume of a cube of side 4 units. Slide the side to explore.
Reveal answer ↓
What it is
The volume of a cube is the length of its edge raised to the power three.
Answer
Volume = side x side x side = 4^3 = 64 cubic units. Since the edge is cubed, even a small increase in the side makes the volume grow quickly.
V = side^3
- •Volume = side^3
- •Unit: cubic units
- •Cubing the edge makes volume grow fast
Why learn this
It measures the space in cubic boxes, dice and storage cubes.
💡 Memory trick
Volume = side^3. Three equal edges multiply.
MathematicsMensurationeasyFind the circumference of a circle of radius 7 units (pi = 3.14159). Slide to explore.
Reveal answer ↓
What it is
The circumference is the distance around a circle, equal to 2 x pi x radius.
Answer
Circumference = 2 x pi x r = 2 x 3.14159 x 7 = 43.98 units. Unlike the area, the circumference grows in direct proportion to the radius - double the radius and you double the distance around.
C = 2 x pi x r
- •Circumference = 2 x pi x r
- •Unit: units of length
- •Grows in proportion to the radius
Why learn this
It's how we measure wheels, pipes and running tracks.
💡 Memory trick
Circumference = 2 x pi x r. Grows in step with the radius.
MathematicsMensurationeasyFind the perimeter of a rectangle 5 units long and 3 units wide. Slide to explore.
Reveal answer ↓
What it is
The perimeter of a rectangle is twice the sum of its length and breadth.
Answer
Perimeter = 2 x (length + breadth) = 2 x (5 + 3) = 2 x 8 = 16 units. Because a rectangle has two lengths and two breadths, we add one of each and double the total.
P = 2 x (length + breadth)
- •Perimeter = 2 x (length + breadth)
- •Two lengths and two breadths
- •Unit: units of length
Why learn this
It's the fencing or border needed around a rectangular field or frame.
💡 Memory trick
Perimeter = 2 x (length + breadth).
MathematicsMensurationeasyFind the perimeter of a square of side 6 units. Slide the side to explore.
Reveal answer ↓
What it is
The perimeter of a square is four times the length of one side.
Answer
Perimeter = 4 x side = 4 x 6 = 24 units. Since a square has four equal sides, we simply multiply one side by four.
P = 4 x side
- •Perimeter = 4 x side
- •Four equal sides
- •Unit: units of length
Why learn this
It's the border or fence needed around a square plot or tile.
💡 Memory trick
Perimeter = 4 x side - four equal sides.
MathematicsMensurationeasyFind the perimeter of a triangle with sides 3, 4 and 5 units. Slide to explore.
Reveal answer ↓
What it is
The perimeter of a triangle is the sum of the lengths of its three sides.
Answer
Perimeter = a + b + c = 3 + 4 + 5 = 12 units. For any triangle, the perimeter is just the sum of its three side lengths.
P = a + b + c
- •Perimeter = a + b + c
- •Add all three sides
- •Unit: units of length
Why learn this
It's the total boundary of any triangular shape.
💡 Memory trick
Perimeter = a + b + c.
MathematicsMensurationeasyFind the area of a parallelogram with base 10 and height 6 units. Slide to explore.
Reveal answer ↓
What it is
The area of a parallelogram is its base multiplied by its perpendicular height.
Answer
Area = base x height = 10 x 6 = 60 square units. The height must be the perpendicular distance between the base and its opposite side, not the length of the slanting side.
A = base x height
- •Area = base x height
- •Use the perpendicular height
- •Unit: square units
Why learn this
It generalises the rectangle's area to slanted shapes.
💡 Memory trick
Area = base x height (use the perpendicular height).
MathematicsMensurationmediumFind the area of a rhombus with diagonals 8 and 6 units. Slide to explore.
Reveal answer ↓
What it is
The area of a rhombus is half the product of its two diagonals.
Answer
Area = 1/2 x d1 x d2 = 1/2 x 8 x 6 = 24 square units. This works because the diagonals of a rhombus bisect each other at right angles, splitting it into four right triangles.
A = 1/2 x d1 x d2
- •Area = 1/2 x d1 x d2
- •Diagonals meet at right angles
- •Unit: square units
Why learn this
It's used for kite-shaped and diamond-shaped figures.
💡 Memory trick
Area = 1/2 x d1 x d2 (the diagonals).
MathematicsMensurationeasyFind the circumference of a circle of diameter 7 units (pi = 3.14159). Slide to explore.
Reveal answer ↓
What it is
The circumference of a circle is pi times its diameter.
Answer
Circumference = pi x diameter = 3.14159 x 7 = 21.99 units. Because the diameter is twice the radius, this is exactly the same as 2 x pi x r. In fact pi is defined as the ratio of the circumference to the diameter.
C = pi x diameter
- •Circumference = pi x diameter
- •Same as 2 x pi x r
- •pi = circumference / diameter
Why learn this
It's the most direct way to find the distance around a circle from its width.
💡 Memory trick
Circumference = pi x diameter (= 2 pi r).
MathematicsMensurationmediumFind the area of a trapezium whose parallel sides are 12 cm and 8 cm and the distance between them is 5 cm.
Reveal answer ↓
What it is
The area of a trapezium is half the sum of its parallel sides times the distance between them.
Answer
Area of a trapezium = 1/2 x (sum of parallel sides) x height = 1/2 x (12 + 8) x 5 = 1/2 x 20 x 5 = 50 cm^2. So the area is 50 square centimetres.
Area of trapezium = 1/2 x (sum of parallel sides) x height
- •Area = 1/2 x (a + b) x h
- •a = 12, b = 8, h = 5
- •1/2 x 20 x 5 = 50
- •Area = 50 cm^2
Why learn this
Many fields and plots have a trapezium shape.
💡 Memory trick
Area = 1/2 x (sum of parallel sides) x height.
MathematicsMensurationmediumFind the area of a rhombus whose diagonals are 16 cm and 12 cm.
Reveal answer ↓
What it is
The area of a rhombus is half the product of its two diagonals.
Answer
Area of a rhombus = 1/2 x d1 x d2, where d1 and d2 are the diagonals. Here = 1/2 x 16 x 12 = 1/2 x 192 = 96 cm^2. So the area of the rhombus is 96 square centimetres.
Area of rhombus = 1/2 x d1 x d2
- •Area = 1/2 x d1 x d2
- •d1 = 16, d2 = 12
- •1/2 x 192 = 96
- •Area = 96 cm^2
Why learn this
It is a quick way to find the area of kite- and diamond-shaped figures.
💡 Memory trick
Area of a rhombus = 1/2 x d1 x d2 (half the product of the diagonals).
MathematicsMensurationmediumFind the total surface area of a cuboid of length 8 cm, breadth 5 cm and height 3 cm.
Reveal answer ↓
What it is
The total surface area of a cuboid is 2(lb + bh + hl).
Answer
Total surface area of a cuboid = 2(lb + bh + hl). Here lb = 8 x 5 = 40, bh = 5 x 3 = 15, hl = 3 x 8 = 24. Sum = 40 + 15 + 24 = 79. Total surface area = 2 x 79 = 158 cm^2.
Total surface area of cuboid = 2(lb + bh + hl)
- •TSA = 2(lb + bh + hl)
- •lb=40, bh=15, hl=24
- •Sum = 79
- •TSA = 158 cm^2
Why learn this
It tells how much material is needed to cover a box on all sides.
💡 Memory trick
Add the three face products lb, bh, hl and double the total.
MathematicsMensurationmediumFind the volume of a cylinder of radius 7 cm and height 10 cm. (Take pi = 22/7.)
Reveal answer ↓
What it is
The volume of a cylinder is the base area times the height, that is pi r^2 h.
Answer
Volume of a cylinder = pi r^2 h = (22/7) x 7^2 x 10 = (22/7) x 49 x 10 = 22 x 7 x 10 = 1540 cm^3. So the volume is 1540 cubic centimetres.
Volume of cylinder = pi r^2 h
- •Volume = pi r^2 h
- •r = 7, h = 10, pi = 22/7
- •(22/7) x 49 x 10 = 1540
- •Volume = 1540 cm^3
Why learn this
It tells how much a pipe, tank or can can hold.
💡 Memory trick
Volume of a cylinder = pi x r^2 x h (circle area times height).
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