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Stage 5.1-3

7.04 Volume and units

Worksheet
Volume unit conversions
1

The cube shown in the diagram has a volume of 1\text{ cm}^3:

Find its volume in \text{mm}^3.

2

Describe how to convert a volume in cubic centimetres to get the volume in cubic metres.

3

Convert the following as indicated:

a
5000\text{ mm}^3 to \text{cm}^3
b
13\text{ cm}^3 to \text{mm}^3
c
58\text{ m}^3 to \text{cm}^3
d
17\,000\,000\text{ cm}^3 to \text{m}^3
e

4\text{ m}^3 to \text{mm}^3

f

2.5\text{ cm}^3 to \text{mm}^3

g

44\,700\text{ mm}^3 to \text{cm}^3

h

3.61\text{ m}^3 to \text{cm}^3

i

9.5\text{ m}^3 to \text{mm}^3

j

76\,210\,000\text{ cm}^3 to \text{m}^3

k

120\,000\,000\text{ mm}^3 to \text{m}^3

l

9\,040\,000\,000\text{ mm}^3 to \text{m}^3

Similar volumes
4

A rectangular prism has a base area of 28\text{ cm}^2 and a height of 7\text{ cm}. If the dimensions of the base are both doubled, find the volume of the rectangular prism.

5

A blue postage box has a base area of 65\text{ cm}^2 and a height of 13\text{ cm}. A red postage box has the same height but triple the base dimensions of the blue box.

a

Find the volume of the red postage box.

b

How many of the blue postage boxes can fit into the red postage box?

6

Noah has a jewellery box with a height of 3\text{ cm} and a base area of 14\text{ cm}^{2} . He wants to build a new jewellery box with dimensions double that of his current jewellery box.

a

Find the height of his new jewellery box.

b

Find the base area of his new jewellery box.

c

Find the volume of Noah's new jewellery box.

d

How many times larger will the volume of Noah's new jewellery box be compared to his current one?

7

Isabelle has a fish tank with a height of y\text{ cm} and a base area of x\text{ cm}. She wants to build a new fish tank with dimensions four times larger than that of her current fish tank.

Find the following:

a

The height of her new fish tank.

b

The base area of her new fish tank.

c

The volume of Isabelle's new fish tank.

d

How many times larger will the volume of Isabelle's new fish tank be compared to her current one?

8

There are two types of cylindrical juice cans available for Lyn to purchase at his local store. One has a diameter of 16\text{ cm} and a height of 18\text{ cm}, and the other has a twice the diameter and height of the smaller can.

a

What is the volume of the smaller can?

b

What is the volume of the bigger can?

c

How many times larger is the volume of the bigger can compared to the smaller one?

Applications
9

The following figure is the outline of a trapezium-shaped block of land:

a

Find the area of the block of land.

b

During a heavy storm, 41\text{ mm} of rain fell over the block of land.

Find the volume of water landed on the property in litres.

10

The roof of a house is flat and measures 19\text{ m} by 16\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 5\text{ mm} of rain falls from the roof. How many litres of rainfall are not collected as a result?

11

Locker A is 50\text{ cm} long, 35\text{ cm} wide and 180\text{ cm} tall. Locker B is 0.55\text{ m} long, 350\text{ mm} wide and 165\text{ cm} tall. Which locker has the most storage?

12

A special medical refrigerator used to store medical samples has dimensions 56\text{ cm} by 42\text{ cm} by 28\text{ cm}. The samples stored in small containers have dimensions 40\text{ mm} by 30\text{ mm} by 20\text{ mm}. We wish to know how many samples can fit in the fridge.

a

Find the volume of one of the sample containers.

b

Find the volume of the fridge in cubic millimetres.

c

How many containers can be stored in the fridge?

13

A box of tissues is in the shape of a rectangular prism. It measures 19\text{ cm} by 0.39\text{ m} by 11\text{ cm}.

a

What is 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 0.95\text{ m} long, what is the maximum number of tissues boxes that can be organised in this way?

14

A cylindrical spa has a radius of 1.8\text{ m} and the water is 160\text{ cm} deep. Find the volume of water in the spa in litres. Round your answer to two decimal places.

15

A cylindrical candle has a radius of 46\text{ mm} and a height of 0.13\text{ m}. Find the volume of the candle in cubic centimetres. Round your answer to two decimal places.

16

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 \text{m}^3 that will be needed to fill up the garden bed.

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Outcomes

MA5.2-12MG

applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

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