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5. Surface Area and Volume
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AustraliaNSW
Year 11

5.035 Volume of pyramids

Lesson
Worksheet
Practice
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 with a rectangular base has four triangular faces. The base has a side measuring $3$3 $cm$cm horizontally and a side measuring $9$9 $cm$cm vertically. A slant height, represented by a dashed line and measuring $14$14 $cm$cm, extends from the apex to the midpoint of the $9$9-$cm$cm side, positioned at the center of the corresponding triangular face. The figure is constructed with solid lines for visible edges and dashed lines to indicate hidden edges.

  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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