Topics
5. Surface Area and Volume
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AustraliaNSW
Year 11

5.035 Volume of pyramids

Lesson
Worksheet
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Lesson

 

Volume of pyramids

The volume of a pyramid with a base area, $A$A,  and height, $h$h, is given by the formula:

Volume of a pyramid
Volume of pyramid $=$= $\frac{1}{3}\times\text{area of base }\times\text{height }$13​×area of base ×height
$V$V $=$= $\frac{1}{3}Ah$13​Ah

The height of the prism must be perpendicular to the base when using this formula. If we are given a slant height, we'll need to use Pythagoras' theorem to work out the vertical height for the volume calculation.

 

Practice questions

QUESTION 1

Find the volume of the rectangular pyramid shown.

A rectangular pyramid with a dashed line representing the height of 5 cm drawn perpendicularly from the apex to the base. The base is a rectangle. The length of the base is marked with single hash marks and measures 8 cm. The width of the base is marked with double hash marks and measures 12 cm. The point where the height meets the base is indicated by a right angle symbol.

QUESTION 2

We wish to find the volume of the following right pyramid.

A right pyramid has a rectangular base. The base has side lengths labeled $3$3 cm along the front edge and $9$9 cm along the right side edge. From the apex of the right pyramid, a dashed line extends diagonally down the right triangular face to the midpoint of the rectangle's $9$9-cm side edge, forming the slant height of the right pyramid. The slant height of the right pyramid is labeled $14$14 cm.

  1. First find the vertical height, correct to two decimal places.

  2. Hence find the volume to one decimal place

Question 3

A rectangular pyramid has a volume of $288$288 cm3. The base has a width of $12$12 cm and length $6$6 cm. Find the height $h$h of the pyramid.

Outcomes

MS11-4

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

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