Volume is the measure of the amount of space inside a solid 3D

figure. It is measured in cubic centimetres/metres etc.

To find a volume of a cube or cuboids, we multiply the length

by the breadth by the height, and for other shapes you

multiply the area of the cross section

by the height. length

breadth

height

Shapes can be 2 dimensional (2-D) or 3 dimensional (3-D).

2-D shapes are slices of 3-D shapes.

e.g. A Cube (3D) = A Square (2D)

Step-by-Step

1. Remember that

volume=length*breadth*height!!!

2. Multiply the length by breadth by

height!

3. Calculate whatever is easiest, e.g.

do 4*2 first, then multiply the

answer by the remaining number

(which is 3.)

4. So you have the sum 8*3, which

gives you 24.

5. Write down your answer using

units cubed!

Example

1. l*b*h

2. 4*2*3

3. 4*2=8

4. 8*3= 24

5. Answer= 24cm3

Step-by-Step

1. Remember that the area of a

triangle is the area of a cross

section.

2. Multiply the area of the cross

section or one end by the length

of the prisms.

3. Remember to half the base then

multiply by the perpendicular

height (from the middle to the

point).

4. Answer using cubic centimetres.

Example B

1. (∏*r2)*h

2. (∏ *22)*7

3. ∏* 22 = 12.562

4. 12.56*7= 87.93

5. Answer= 87.92cm3

Step-by-Step

1. Remember that volume=

(r2*∏)*h!!!!

2. Multiple the length by the radius

squared.

3. Calculate whatever is easiest, e.g.

Do r2*∏ first, then multiply the

answer by the remaining number

(which is 7.)

4. So you have the sum 12.56*7,

which gives you 87.92.

5. Remember that pi = aprox. 3.14.

Step-by-Step

1. Remember that volume of cubes

or cuboids is l*b*h.

2. Separate the shape into several

individual ones.

3. Work out the volume of each

using length*breadth*height.

4. Add them all together.

5. The answer should be in cm3.

Work out irregular

shapes

such as this exactly the

same way as cubes or

cuboids,

length*breadth*height

Work out each

individual and then add

them together.

Questions

1. Find the volume of a cylinder of height 9cm and

diameter 7cm (r=d/2)

2. What is the volume of the below cylinder?

3. Find the volume of the cuboid below.

4. Find the volume of the triangular prism below.

Answers1. Find the volume of a cylinder of height 9cm and diameter 7cm (r=d/2)

Answer: 98.91cm3

2. What is the volume of the below cylinder?

Answer: 188.4cm3

3. Find the volume of the cuboid below.

Answer: 108cm³

4. Find the volume of the triangular prism below.

Answer: 24cm³

Extension Activities

(a) What is the volume of a

cylinder of height 1cm and radius

1cm?

(b) What is the volume of a

cylinder of height 2cm and radius

2cm?

(c) Continue this pattern to 10

and note the answers.

Extension ActivitiesAnswers(a)What is the volume of a

cylinder of height 1cm and radius 1cm?

Answer: 3.14

(b) What is the volume of a cylinder of height 2cm and radius 2cm?

Answer: 25.13

(c) Continue this pattern to 10 and note the answers.

Answer: 84.82

Extension ActivitiesIf the length of the prism is 8 and the

width of the base is 4 work out the height using the following sum.

2*?*8=60cm3 2*8=1660/16= 3.75

Press to reveal answer

Conclusion

To work out the volume of a cylinder:

• Find the area of the circle (∏*r2) • Multiply this by the height of the

cylinder

Simple really!!!!

Conclusion

To work out the volume of a triangular prism:

• Find the area of the cross section (1/2

base *height) • Multiply this by the height of the

prism

Easy!

Conclusion

To work out the volume of a cube or cuboid:

• Multiply the length the breadth and the height.

• Or area of cross section times height.

Childs play!!!!

ConclusionTo work out the volume of an irregular

shape:• Separate the shape into individual ones.• Multiply the length the breadth and the

height of each separate shape.• Or area of cross section times height.• Then add them together.

Oh!!!

ConclusionJust remember these simple steps and you will

find it easy.