2D AREA BASICS
Find the area of a rectangle with length 8 cm and width 5 cm.
Area = 40 cm².
Find the surface area of a cube with side length 4 cm.
SA = 6(4²) = 96 cm².
Find the volume of a cube with side length 5 cm.
V = 125 cm³.
A football pitch measures 100 m by 70 m.
Find its area.
Area = 7000 m².
A triangle has base 10 cm and height 7 cm. Find its area.
Area = 35 cm².
A rectangular box has dimensions 3 cm × 5 cm × 7 cm.
Find its total surface area.
SA = 2(lw + lh + wh) = 2(15 + 21 + 35) = 142 cm².
A cylinder has radius 3 cm and height 12 cm.
Find its volume (in terms of π).
V = πr²h = π(9)(12) = 108π cm³.
A garden bed is 3 m wide and has an area of 21 m².
How long is it?
Length = 7 m.
Find the circumference of a circle with radius 6 cm.
(Give your answer in terms of π.)
C = 12π cm.
A cylinder has radius 4 cm and height 9 cm.
Write the formula for total surface area (don’t calculate).
SA = 2πr² + 2πrh.
A cone has radius 5 cm and height 9 cm.
Find its volum
V = 1/3 πr²h = (1/3)π(25)(9) = 75π cm³.
A water tank is a cylinder with radius 2 m and height 4 m.
Find how many cubic metres of water it can hold.
V = π(4)(4) = 16π m³.
A circle has radius 5 cm. Find the area of a 90° sector.
Area = (90/360) × π(5²) = 25π/4 cm²
A cone has radius 3 cm and slant height 10 cm.
Find the lateral surface area.
LSA = πrl = π(3)(10) = 30π cm².
A sphere has radius 4 cm.
Find its volume (in terms of π).
V = (4/3)πr³ = (4/3)π(64) = 256π/3 cm³.
A cone has slant height 13 cm and radius 5 cm.
Use Pythagoras to find the vertical height.
h² = 13² − 5² = 144 → h = 12 cm.
A trapezoid has parallel sides 12 cm and 18 cm, with a height of 10 cm.
Find the area.
Area = ½(12 + 18)(10) = 150 cm².
A sphere has radius 6 cm.
Find its surface area.
SA = 4πr² = 144π cm².
A triangular prism has cross-sectional area 24 cm² and length 15 cm.
Find its volume.
V = area of base × length = 360 cm³.
You want to paint a cylindrical tub (including the top and bottom).
Radius = 3 m, height = 5 m.
Find the total area you need to paint.
SA = 2πr² + 2πrh
= 18π + 30π
= 48π m².