Tyler built a dollhouse for his sister as shown in the diagram below.

Question

The diagram shows a rectangular prism with a length of 4 ft, a width of 3 ft, and a height of 2 ft. Above it is a pyramid with the same length and width as its base, but the height of the pyramid is 1.5 ft.

Find the volume of the dollhouse. Round your answer to the nearest tenth. Show all work in order to receive full credit.

Answer 1

To find the volume of the dollhouse, we need to find the volume of the rectangular prism and the volume of the pyramid, and then add them together.

Volume of rectangular prism:
length = 4 ft
width = 3 ft
height = 2 ft

Volume = length x width x height
Volume = 4 ft x 3 ft x 2 ft
Volume = 24 ft³

Volume of pyramid:
length of base = 4 ft
width of base = 3 ft
height = 1.5 ft

Volume = 1/3 x base area x height
Base area = length x width = 4 ft x 3 ft = 12 ft²
Volume = 1/3 x 12 ft² x 1.5 ft
Volume = 6 ft³

Total volume of dollhouse:
24 ft³ (prism) + 6 ft³ (pyramid) = 30 ft³

Therefore, the volume of the dollhouse is 30 cubic feet.