Volume of Pyramids Examples

Find the volume of the square pyramid.

To find the volume, we need the height of the entire pyramid, not the slant height of the lateral faces. If the slant height is the hypotenuse, the bottom leg is 10 meters and the Pythagorean Theorem will give us the rest.

a² + b² = c²
(10 m)² + h² = (14.14 m)²
h ≈ 10 m

Armed with the height, we're fully equipped to calculate the volume of this pyramidal puppy.

V ≈ 1333.3 m³

The sweet smell of success.

Find the volume of this regular (but not right) pentagonal pyramid.

The pyramid might be oblique, but we don't treat it any differently. We still use the same formula, only this time finding the area of the base might be a bit trickier.

Splitting up the pentagon into five identical triangles should do the job. Then, we can calculate the area of each triangle and multiply it by 5.

B = 37.5 ft²

Plug that guy into our volume equation and that's all there is to it.

V = 912.5 ft³