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