Area Bounded by a Circle, Surface Area and Volume of Some Solids
Primary 6 · Mathematics
Area Bounded by a Circle, Surface Area and Volume of Some Solids
Lesson 5 of 5
18 min
Let's begin
Uwase's mother sells beans at Kimironko market. She keeps them in a wooden box 30 cm long, 20 cm wide and 15 cm deep. A customer asks: "How much does that box hold?"
That is a question about volume: how much space is inside a solid. By the end of this lesson you will answer it in two ways, in cubic centimetres and in litres.
Volume is the amount of space a solid takes up. We measure it in cubic units. A cube with edges of 1 cm has a volume of 1 cm³ (one cubic centimetre). Bigger things are measured in m³.
Imagine filling a box with 1 cm cubes. If the floor of the box is 4 cm by 3 cm, one layer holds 4 × 3 = 12 cubes. If the box is 5 cm tall, it holds 5 layers: 12 × 5 = 60 cubes, so its volume is 60 cm³.
That is why: volume of a cuboid = length × width × height, which is the same as area of the base × height.
A cube has all three edges equal: volume of a cube = side × side × side. For a cube with 6 cm edges: 6 × 6 × 6 = 216 cm³.
Worked example 1
the bean box.
Worked example 2
a water tank 2 m long, 1.5 m wide and 1 m high.
Worked example 3
a box has a volume of 3 600 cm³. It is 20 cm long and 15 cm wide. How high is it?
Worked example 4
a cube has a volume of 125 cm³. Which number times itself three times makes 125? 5 × 5 × 5 = 125, so each edge is 5 cm.
Worked example 5
a box is 12 cm × 8 cm × 5 cm.
Any face times the edge that is not on it gives the volume: 96 × 5 = 60 × 8 = 40 × 12 = 480 cm³.
The rule "area of base × height" works for every prism. A triangular prism whose triangle has an area of 6 cm² and which is 10 cm long has a volume of 6 × 10 = 60 cm³.
It works for a cylinder too, whose base is a circle: volume of a cylinder = π × r × r × h. A tin with r = 4 cm and h = 10 cm holds 3.14 × 4 × 4 × 10 = 502.4 cm³.
Tip
Volume = floor × height. Work out how much covers the floor (the base area), then stack that many layers up to the top.
And remember: 1 000 cm³ = 1 litre, and 1 m³ = 1 000 litres.
Answers
What you learned today
Sources and credits
The bean-box and water-tank stories and all the worked examples were written by Ganzaa.
Quick check
A box is 10 cm long, 6 cm wide and 4 cm high. What is its volume?
