Tyler built a dollhouse for his sister as shown in the diagram below. Find the volume of the dollhouse. Round your answer to the nearest tenth. Show all work in order to receive full credit. You may upload a picture of your work.

Answer 1

In order to find the volume of the dollhouse, we need to find the volume of each individual shape and then add them all together.

1. The base of the dollhouse is a rectangular prism with dimensions 12 inches by 18 inches by 3 inches.
Volume of the base = length x width x height = 12 in x 18 in x 3 in = 648 cubic inches

2. The roof of the dollhouse is a triangular prism with base dimensions 12 inches by 18 inches and height 5 inches.
Volume of the roof = 1/2 x base x height x height = 1/2 x 12 in x 18 in x 5 in = 540 cubic inches

3. The front of the dollhouse is a triangular prism with base dimensions 6 inches by 12 inches and height 9 inches.
Volume of the front = 1/2 x base x height x height = 1/2 x 6 in x 12 in x 9 in = 324 cubic inches

Adding the volumes of the base, roof, and front together:
Total volume = 648 cubic inches + 540 cubic inches + 324 cubic inches = 1512 cubic inches

Therefore, the volume of the dollhouse is 1512 cubic inches.