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 2 ft, and a height of 3 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

First, let's find the volume of the rectangular prism:

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

Next, let's find the volume of the pyramid:

Volume of pyramid = 1/3 x base area x height
Base area = length x width = 4 ft x 2 ft = 8 ft²
Volume = 1/3 x 8 ft² x 1.5 ft
Volume = 4 ft³

Now, let's find the total volume of the dollhouse by adding the volume of the rectangular prism and the volume of the pyramid:

Total volume = volume of rectangular prism + volume of pyramid
Total volume = 24 ft³ + 4 ft³
Total volume = 28 ft³

Therefore, the volume of the dollhouse is 28 cubic feet.