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5.035 Volume of pyramids

Worksheet
Volume of pyramids
1

Find the volume of the following pyramids:

a
b
c
d
e
f
2

Consider the following right pyramid:

a

Find the perpendicular height of the pyramid. Round your answer to two decimal places.

b

Hence, find the volume of the pyramid. Round your answer to two decimal places.

3

A right pyramid has a square base of 24 \text{ mm} and a perpendicular height of 24 \text{ mm}. Find the volume of the pyramid.

4

A pyramid with a height of 7 m has a right-angled triangular base with side lengths 6 m, 8 m and 10 m. Find the volume of the pyramid.

5

A rectangular pyramid has a volume of 288 \text{ cm}^{3}. The base has a width of 12 \text{ cm} and length 6 \text{ cm}. Find the height of the pyramid.

6

A square pyramid has a base with side length 12\text{ mm} and a volume of 1248\text{ mm}^3. Find the height of the pyramid.

7

A square pyramid has a height of 24\text{ cm} and a volume 2592\text{ cm}^3. Find the base side length of the pyramid.

8

The Great Pyramid is a right pyramid. It has a square base of side length 230 \text{ m} and a vertical height of 146 \text{ m}. Find the volume of the Great Pyramid. Round your answer to the nearest tenth of a cubic metre.

9

Find the capacity of the pyramid shown. Round your answer to the nearest tenth of a cubic centimetre.

Applications
10

A paperweight is in the shape of a square pyramid with dimensions as shown. The paperweight is filled with solid glass.

Find the volume of glass needed to make 3000 paperweights.

11

Consider the following bottles of portable hand wash. Assume that their volumes are equivalent to pyramids of the same dimensions.

a

By approximately what factor is the amount of hand wash in bottle B greater than in bottle A?

b

If bottle A costs \$50.88 and bottle B costs \$60.00, which is the better buy?

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Outcomes

MS11-4

performs calculations in relation to two-dimensional and three-dimensional figures

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