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.

Answer 1

To find the volume of the dollhouse, we need to calculate the volume of each individual piece and then add them together.

1. The base of the dollhouse is a rectangle with dimensions 12 inches by 20 inches. The height of the base is 1 inch.
Volume of base = length x width x height
Volume of base = 12 in x 20 in x 1 in = 240 cubic inches

2. The roof of the dollhouse is a triangle with base 14 inches and height 8 inches.
Volume of roof = (1/2) x base x height
Volume of roof = (0.5) x 14 in x 8 in = 56 cubic inches

3. The front and back walls of the dollhouse are rectangles with dimensions 12 inches by 8 inches.
Volume of front and back walls = length x width x height
Volume of front and back walls = 2 x (12 in x 8 in x 1 in) = 192 cubic inches

4. The side walls of the dollhouse are rectangles with dimensions 20 inches by 8 inches.
Volume of side walls = length x width x height
Volume of side walls = 2 x (20 in x 8 in x 1 in) = 320 cubic inches

Therefore, the total volume of the dollhouse is the sum of the volumes of the base, roof, front and back walls, and side walls:
240 cubic inches (base) + 56 cubic inches (roof) + 192 cubic inches (front and back walls) +320 cubic inches (side walls) = 808 cubic inches

Therefore, the volume of the dollhouse is 808 cubic inches.