Find the volume of a regular square pyramid whose square base has edge 15 m and whose height is 8 m.

Step-by-step solution

1. 1

   Write the pyramid volume formula. For any pyramid, whatever the base shape,

   $V=\frac{1}{3}Bh,$

   where $B$ is the area of the base and $h$ is the perpendicular height from the apex to the base plane.

2. 2

   Compute the base area. The base is a square of edge $15\ \text{m}$:

   $B=15^{2}=225\ \text{m}^2.$

3. 3

   Substitute the height. The height given is $h=8\ \text{m}$. Take care not to confuse this with the slant height, which runs along a triangular face and would be longer; only the perpendicular height belongs in this formula.

4. 4

   Multiply and divide by three.

   $V=\frac{1}{3}(225)(8)=\frac{1800}{3}=600\ \text{m}^3.$

5. 5

   Interpret the one third. A prism on the same square base with the same height would hold $225\times 8=1800\ \text{m}^3$; the pyramid holds exactly one third of that, $600\ \text{m}^3$. Checking that your pyramid answer is one third of the matching prism is a fast way to catch a dropped factor.