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.
The Doll house is made up of a pyramid and a rectangule prism.
The Pyramid height is 1.5 ft
The rectangular prism ha a base length of 4 ft and 3 ft with a height of 2 ft
First, we need to find the volume of the pyramid.
Volume of a pyramid = (1/3) * base area * height
The base of the pyramid is a rectangle with dimensions 4 ft by 3 ft
Base area of the pyramid = 4 ft * 3 ft = 12 ft^2
Volume of the pyramid = (1/3) * 12 ft^2 * 1.5 ft = 6 ft^3
Next, we need to find the volume of the rectangular prism.
Volume of a rectangular prism = base area * height
Base area of the rectangular prism = 4 ft * 3 ft = 12 ft^2
Volume of the rectangular prism = 12 ft^2 * 2 ft = 24 ft^3
Now, we add the volumes of the pyramid and the rectangular prism to find the total volume of the dollhouse.
Total volume = 6 ft^3 + 24 ft^3 = 30 ft^3
Therefore, the volume of the dollhouse is 30 cubic feet.