Volume of Solids
Senior 2 · Mathematics
Volume of Solids
Lesson 2 of 4
20 min
Look around any Rwandan town and you will see cylinders: plastic rainwater tanks beside houses, milk cans at dairy cooperatives, water pipes, tins of tomato paste. A cylinder is a prism with a circular cross-section, so you already know how to find its volume.
A cylinder has two equal parallel circular faces of radius r, a distance h apart.
Like any prism, its volume is base area × height. The base is a circle of area πr2, so
V = πr2h.
In this unit, use π = 3.14 unless the question says otherwise, or leave the answer in terms of π.
Worked example 1
a rainwater tank. A cylindrical tank has radius 0.8 m and height 2 m. How many litres does it hold?
V = 3.14 × 0.82 × 2 = 3.14 × 0.64 × 2 = 4.0192 m3. Since 1 m3 = 1000 L, the tank holds about 4,019 litres, roughly 4 m3.
Worked example 2
finding a height. A dairy cooperative's cylindrical milk can holds 20 litres and has a radius of 14 cm. How tall is it inside?
20 L = 20,000 cm3. So 3.14 × 142 × h = 20,000, which gives 615.44h = 20,000 and h = 20,000 ÷ 615.44 ≈ 32.5 cm.
Worked example 3
in terms of π. A tin has diameter 10 cm and height 12 cm. The radius is half the diameter, r = 5 cm, so V = π × 25 × 12 = 300π cm3.
Tip
Exam technique. Read carefully whether you are given the radius or the diameter. If it is the diameter, halve it before squaring. Square only the radius, not π or h: πr2h means π × r × r × h.
Find the volume of a cylinder with radius 7 cm and height 10 cm (π = 3.14).
Solution: 3.14 × 49 × 10 = 1,538.6 cm3.
A cylinder has radius 5 cm and volume 1,570 cm3. Find its height (π = 3.14).
Solution: 3.14 × 25 × h = 1,570, so 78.5h = 1,570 and h = 20 cm.
A pipe has an inside diameter of 4 cm and is 3 m long. Find the volume of water it holds, in terms of π.
Solution: r = 2 cm and h = 300 cm. V = π × 4 × 300 = 1,200π cm3 (about 3.8 litres).
Remember
Sources and credits
The Rwandan worked examples, the practice items and the exercises were written by Ganzaa.
