Question

A rectangular pyramid fits exactly on top of a rectangular prism. Find the volume of the composite space figure if the prism has a length of 14 centimeters, a width of 3 centimeters, a height of 16 centimeters, and the pyramid has a height of 15 centimeters.

Answer 1

First we calculate for the volume of the prism,
V = Length x width x height
V = (14 cm) x (3 cm) x (16 cm) = 192 cm³
Then, we calculate for the volume of the pyramid through the equation,
V = (1/3)(Bh)
where B is the area of the base that in this sample is equal to 42 cm².
Substituting,
V = (1/3)(42 cm²)(15 cm) = 210 cm³
Then, adding both volumes we have 402 cm³ composite figure.