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4.07 Volume of prisms

Worksheet
Rectangular prisms
1

Find the volume of the following prisms:

a
b
c
d
e
f
2

Find the volume of the cube shown:

3

Find the volume of a cube with the following side lengths:

a
5 \text{ cm}
b
4 \text{ mm}
4

The following rectangular prism has a volume of 168\text{ mm}^3:

Find the length, a, of the rectangular prism.

5

The following rectangular prism has a volume of 1680\text{ mm}^3:

Find the width of the rectangular prism in millimetres.

6

The following rectangular prism has a volume of 1224\text{ m}^3:

Find the length, b, of the rectangular prism in metres.

7

The following rectangular prism has a volume of 300\text{ mm}^3:

Find the height, a, of the rectangular prism in millimetres.

8

The following rectangular prism has a volume of 162\text{ mm}^3:

Find the width, a, of the rectangular prism in millimetres.

9

The following rectangular prism has a volume of 510\text{ mm}^3:

Find the length, t, of the rectangular prism in millimetres.

10

Find the length of the rectangular prism with volume 162\text{ cm}^3, width 6\text{ cm} and height 3\text{ cm}.

11

Find the side length of a cube with volume 27\text{ cm}^3.

12

Each face of a cube has an area of 64\text{ cm}^{2}.

a

Find the length of the cube's edge.

b

Find the volume of the cube.

Triangular prisms
13

Find the volume of the following prisms:

a
b
c
d
e
f
g
14

Consider the following triangular prism:

a

Find the volume of the prism.

b

Find the capacity of the prism.

15

The volume of the triangular prism shown is 40.8 \text{ m}^3:

Find the value of p.

16

The volume of the triangular prism shown is 231\text{ cm}^3:

Find the value of k.

17

The volume of the triangular prism shown is 117 \text{ m}^3.

Find the value of y.

18

The volume of the triangular prism shown is 287.5\text{ m}^{3}:

Find the value of k, to one decimal place.

19

The volume of the triangular prism shown is 247.45\text{ cm}^{3}:

Find the value of y to one decimal place.

Applications
20

This nesting box needs to have a volume of 129\,978\text{ cm}^{3}, a height of 83\text{ cm} and a width of 54\text{ cm}. Find the depth, d, of the box.

21

Find the maximum volume of water the following aquarium can hold:

22

A box is 1 \text{ m} long, 20 \text{ cm} high and 30 \text{ cm} wide. What is the volume of the box in cubic centimetres?

23

A container has the shape of a rectangular prism, with the following dimensions: 50\text{ cm}, 80 \text{ cm}, and 20 \text{ cm}. Find its volume.

24

A tank has a length of 7 \text{ m}, width of 2 \text{ m} and depth of 6 \text{ m}. Find the volume of the tank in cubic metres.

25

A box of tissues is in the shape of a rectangular prism. It measures 19 \text{ cm} by 39 \text{ cm} by 11 \text{ cm}.

a

Find the volume of the box.

b

A supermarket owner wants to arrange a number of tissues boxes on a shelf such that there are no gaps between the boxes or at either end of the shelf. If the shelf at the supermarket is 95 \text{ cm} long, find the maximum number of tissues boxes that can be organised in this way.

26

A rectangular swimming pool has a length of 27\text{ m}, width of 14\text{ m} and depth of 3\text{ m}.

Find the capacity of the swimming pool in litres.

27

A container has the shape of a rectangular prism, with the following dimensions: 40 \text{ cm}, 80 \text{ cm}, and 10 \text{ cm} .

a

Find the volume of the container.

b

Find the capacity of the container in litres.

28

A garden bed is 5 \text{ m} in length, 2\text{ m} in width and 20 \text{ cm} in height. Find the volume of soil in cubic metres that will be needed to fill up the garden bed.

29

A rectangular swimming pool has a length of 27 \text{ m}, width of 14 \text{ m} and depth of 3 \text{ m}.

a

Find the volume of the swimming pool.

b

Find the capacity of the swimming pool.

30

A cubic container has a capacity of 153 \text{ mL}.

a

What is the volume of the container in cubic centimetres?

b

Find the side length of the container correct to two decimal places.

31

The roof of a house is flat and measures 16\text{ m} by 15 \text{ m} in the shape of a rectangle.

a

Find the area of the roof.

b

If a water tank collects all the water from the roof, how many litres of water would it collect if there had been 20 \text{ mm} of rain?

c

After the water tank has become full, a further 10 \text{ mm} of rain falls from the roof. How many litres of rainfall are not collected as a result?

32

A refrigerator is used to store medical samples and has dimensions 18 \text{ cm} by 70 cm by 12 \text{ cm}. The samples are stored in small containers in the shape of rectangular prisms that have dimensions 20 \text{ mm} by 50 \text{ mm} by 20 \text{ mm}.

a

Find the volume of a sample container in cubic centimetres.

b

Find the volume of the fridge.

c

Hence, how many containers can be stored in the fridge?

33

Find the volume of concrete required to build the skateboard ramp shown:

34

Find the volume of the following tent in cubic metres:

35

A fish tank designed to sit in the corner of a room has the shape of a right-angled triangular prism.

If its dimensions are as shown in the image, determine the capacity of the fish tank in litres.

36

The volume of the following tent is 4.64\text{ m}^3.

Find the height, h, of the tent.

37

A metal rectangular prism is melted down and re-cast into identical triangular prisms as shown in the images below:

a

If all of the metal is able to be re-used, calculate the number of whole triangular prisms that can be made.

b

If 7\% of the metal is wasted in the process, calculate the number of whole triangular prisms that can be made.

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Outcomes

ACMEM030

calculate the volume of objects, such as cubes and rectangular and triangular prisms

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