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CanadaON
Grade 7

10.04 Volume of prisms and cylinders

Worksheet
Rectangular prisms
1

Find the volume of the following rectangular prisms:

a
b
c
d
e
2

Find the volume of the following cubes:

a
b
3

Explain how to find the volume of a cube that has a side length of 14\text{ m}.

4

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

Mixed prisms
5

For each of the following prisms:

i

State the shape of the prism's base.

ii

Find the area of the prism's base.

iii

Find the volume of the prism.

a
b
6

Find the volume of the following prisms:

a
b
c
d
e
f
7

A triangular prism with a base area of 20 \,\text{cm}^2 and a height of 10 \,\text{cm}. Find its volume.

8

An octagonal prism with a base area of 80 \,\text{mm}^2 and a height of 120 \,\text{mm}. Find its volume.

Volume of cylinders
9

Rochelle notices that the base of a cylinder is always a circle. To save working out time, Rochelle decides to combine the area formula A = \pi r^{2} with the volume formula V = A h.

By substituting the area formula into the volume formula, state the formula Rochelle gets for the volume of a cylinder.

10

Consider the solid shown in the diagram:

a

State the shape of the base of this solid.

b

Find the exact area of the solid's base.

c

Find the exact volume of the solid.

11

Find the volume of the following solids, rounding your answers to one decimal place:

a
b
12

Explain how to get the volume of the following solid to the one decimal place.

Applications
13

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.

14

A box of tissues is in the shape of a rectangular prism. It has a length of 39 \text{ cm}, a width of19 \text{ cm} and a height of 11 \text{ cm}. Find the volume of the box.

15

A tank has a length of 9\text{ m}, width of 4\text{ m} and depth of 8\text{ m} . Find the volume of the tank.

16

A container has the shape of a rectangular prism with dimensions 50\text{ cm}, 30\text{ cm}, and 60\text{ cm}. Find the volume of the container.

17

Find the maximum volume of water this aquarium can hold:

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Outcomes

7.E2.1

Describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm^3) to solve problems.

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