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5.035 Volume of pyramids

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$13Ah

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 is shown. The figure has four triangular faces. The rectangle, serving as the base, has its length measured 3 cm and its width measured $9$9 cm. A slant height represented by a dashed line measuring $14$14 cm is drawn, from the apex through one of the triangle faces to its width that measures 9 cm. The figure is constructed with solid lines for the edges and dashed lines to indicate edges hidden from view.

  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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