Mini-Lesson

Mensuration

This mini-lesson covers Mensuration for Cambridge IGCSE Mathematics (0580): perimeter, area, surface area & volume of prisms, cylinders, spheres, cones and pyramids, and arcs & sectors (Extended content included).

Honest heads-up: these games test recall of formulae and results. Use π ≈ 3.142 and show working in the exam.

Answer as you go and collect ⭐ stars. Press Start.

Area & perimeter

Perimeter is the distance around a shape; area is the space inside. Key areas: rectangle b×h, triangle ½bh, parallelogram b×h, trapezium ½(a + b)h.

circle: area = πr² · circumference = 2πrr = radius, d = 2r

Worked example

Trapezium, parallel sides 5 and 9, height 4: ½(5 + 9)×4 = ½×14×4 = 28.

Calculate

Your turn

1A triangle has base 12 cm and height 7 cm. Work out its area.

cm²

Hint: area = ½ × base × height = ½ × 12 × 7.

Calculate

Your turn

2A circle has radius 5 cm. Work out its area, using π = 3.142. Round to the nearest whole number.

cm²

Hint: area = πr² = 3.142 × 5² = 3.142 × 25.

Prisms & cylinders

Volume of prisms & cylinders

A prism has the same cross-section throughout. Its volume is the cross-section area times the length. A cylinder is a circular prism.

prism: V = area of cross-section × lengthcylinder: V = πr²h

Worked example

Cuboid 3 × 4 × 5: cross-section 3×4 = 12, ×5 = 60 cm³.

Calculate

Your turn

3A cylinder has radius 3 cm and height 10 cm. Work out its volume using π = 3.142. Round to the nearest whole number.

cm³

Hint: V = πr²h = 3.142 × 3² × 10 = 3.142 × 90.

Spheres, cones & pyramids

Learn these standard formulae:

sphere: V = 4/3 πr³ · SA = 4πr²cone: V = ⅓ πr²h, curved SA = πrl · pyramid: V = ⅓ × base × height

Worked example

Cone, r = 3, h = 4: V = ⅓ × π × 9 × 4 = 12π ≈ 37.7 cm³.

Don't mix them up: a cone and pyramid both have the ⅓ factor; a cylinder and prism do not.

Calculate

Your turn

4A square-based pyramid has base area 30 cm² and height 8 cm. Work out its volume.

cm³

Hint: V = ⅓ × base area × height = ⅓ × 30 × 8.

Calculate

Your turn

5A sphere has radius 3 cm. Work out its volume using π = 3.142. Round to the nearest whole number.

cm³

Hint: V = 4/3 × π × r³ = 4/3 × 3.142 × 27.

Quick check

?Which formula gives the volume of a cone with base radius r and height h?

Arcs & sectors

An arc is part of the circumference; a sector is a "pizza slice". Use the fraction θ/360.

arc = (θ/360) × 2πr · sector area = (θ/360) × πr²θ = angle of the sector in degrees

Worked example

Sector, r = 6, θ = 90°: area = (90/360) × π × 36 = ¼ × 36π = 9π ≈ 28.3 cm².

Calculate

Your turn

6A sector has radius 4 cm and angle 90°. Work out its area using π = 3.142. Round to 1 decimal place.

cm²

Hint: (90/360) × π × 4² = ¼ × 3.142 × 16.

Match game

Solid ⇄ volume formula

Tap a solid, then its correct volume formula.

Sort it

Has a ⅓ in the volume?

Sort each solid: does its volume formula include a factor of ⅓? Tap it, then its box.

⅓ Yes (⅓ factor)

✗ No ⅓ factor

Recap

Key points

Area: triangle ½bh, trapezium ½(a+b)h, circle πr².

Prism/cylinder: V = cross-section × length; cylinder πr²h.

Sphere: V = 4/3πr³, SA = 4πr². Cone: V = ⅓πr²h. Pyramid: ⅓ × base × height.

Arc & sector: multiply the full circle by θ/360.

You've covered the Mensuration essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.

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