How do you find the volume of any prism?

area of cross-section × length. The cross-section is the same all the way along.

A cone and a cylinder have the same base and height. How do their volumes compare?

The cone's is one third. A cone is ⅓πr²h.

What is the surface area of a cube with edges of 3 cm?

54 cm². Six faces, each 9 cm².

Volume and surface area · Cambridge IGCSE Mathematics (9

In plain words

Volume is how much space a solid takes up. For anything with the same shape all the way through, a prism, it is the area of the end multiplied by the length. Pointed shapes come to exactly a third of that.

Three things to know

Prism (including a cuboid and a cylinder): volume = area of cross-section × length. Cylinder: πr²h.
Pyramid and cone: ⅓ × area of base × height. Cone: ⅓πr²h. Sphere: 4/3 πr³.
Surface area is the total area of all the faces. Cylinder: 2πrh for the curved part plus 2πr² for the two ends. Sphere: 4πr². Curved surface of a cone: πrl, where l is the slant height.

Worked example

Find the volume of a cylinder of radius 3 cm and height 10 cm.

Volume = πr²h.
= π × 3² × 10 = 90π.
= 283 cm³ (to 3 significant figures).

Tips and tricks

The formulas for the cone, pyramid and sphere are usually given in the exam. The prism and cylinder you are expected to know.
Volume is in cm³; surface area is in cm².

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Volume and surface area: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the volume of a cuboid 2 cm by 3 cm by 5 cm?
- 10 cm³
- 30 cm³ (the answer)
- 31 cm³
- 62 cm³
2 × 3 × 5.
How do you find the volume of any prism?
- add the lengths of its edges
- area of cross-section × length (the answer)
- ½ × base × height
- 4/3 πr³
The cross-section is the same all the way along.
What is the volume of a cylinder with radius 2 cm and height 5 cm?
- 10π cm³
- 20π cm³ (the answer)
- 50π cm³
- 100π cm³
π × 2² × 5.
A cone and a cylinder have the same base and height. How do their volumes compare?
- They are equal.
- The cone's is half.
- The cone's is one third. (the answer)
- The cone's is twice.
A cone is ⅓πr²h.
What is the surface area of a cube with edges of 3 cm?
- 27 cm²
- 36 cm²
- 54 cm² (the answer)
- 9 cm²
Six faces, each 9 cm².

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 11 marks. Write your answers on paper, then check them.

Volume and surface area

Cambridge IGCSE Mathematics (9–1) 0980 · 11 marks · papermunch.org

Name ______________________________ Date ______________

Find the volume of a cuboid 4 cm by 5 cm by 6 cm.[2]
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120 cm³.
I got this one
A triangular prism has a cross-section with base 6 cm and height 4 cm, and a length of 10 cm. Find its volume.[3]
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120 cm³. Area of triangle = 12 cm²; 12 × 10.
I got this one
Find the volume of a cone of radius 3 cm and height 8 cm.[3]
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75.4 cm³. ⅓ × π × 9 × 8 = 24π.
I got this one
Find the total surface area of a cylinder of radius 2 cm and height 5 cm.[3]
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88.0 cm². 2π × 2 × 5 + 2π × 2² = 20π + 8π = 28π.
I got this one

Answers: Volume and surface area

1. 120 cm³.
2. 120 cm³. Area of triangle = 12 cm²; 12 × 10.
3. 75.4 cm³. ⅓ × π × 9 × 8 = 24π.
4. 88.0 cm². 2π × 2 × 5 + 2π × 2² = 20π + 8π = 28π.