Question

Adam has a playhouse in his backyard that is shaped like a square prism with a squarepyramid for the roof. What is the volume of his playhouse if the house is 3 ft x 3 ft x 5 ft high and the roof is 3 ft x 3 ft x 2 ft high

Answer 1

51 cubic feet

Explanation:

This is basically a rectangular prism + pyramid.

Volume of rectangular prism = length * width * height

Volume of square pyramid = 1/3 * area of base * height

The rectangular prism's dimensions are 3 x 3 x 5 , so volume = 3*3*5 = 45

The pyramid's base is a square with side 3, so area of base = 3 * 3 = 9

The height is 2, we find the volume using the formula stated above as:

1/3 * 9 * 2 = 6

Volume of Playhouse = volume of rectangular prism + volume of pyramid

Volume of Playhouse = 45 + 6 = 51 cubic feet