Tyler built a dollhouse for his sister as shown in the diagram below.
The diagram shows a rectangular prism with a length of 4 ft, a width of 2 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.
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:
V = length x width x height
V = 4 ft x 2 ft x 2 ft
V = 16 ft³
Volume of pyramid:
V = 1/3 x base area x height
First we need to find the base area:
Base area = length x width
Base area = 4 ft x 2 ft
Base area = 8 ft²
Now we can find the volume of the pyramid:
V = 1/3 x 8 ft² x 1.5 ft
V = 4 ft³
Now, we add the volume of the rectangular prism and the volume of the pyramid:
V_total = 16 ft³ + 4 ft³
V_total = 20 ft³
Therefore, the volume of the dollhouse is 20 cubic feet.
Sorry, I made a mistake with the given information. Here is the fixed version:
Tyler built a dollhouse for his sister as shown in the diagram below.
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.
No problem! Let's recalculate the volume of the dollhouse with the corrected dimensions:
Volume of rectangular prism:
V_rectangular prism = length x width x height
V_rectangular prism = 4 ft x 3 ft x 2 ft
V_rectangular prism = 24 ft³
Volume of pyramid:
To find the volume of the pyramid, we first need to find the base area:
Base area = length x width
Base area = 4 ft x 3 ft = 12 ft²
Now we can find the volume of the pyramid:
V_pyramid = 1/3 x base area x height
V_pyramid = 1/3 x 12 ft² x 1.5 ft
V_pyramid = 6 ft³
Now, we add the volume of the rectangular prism and the volume of the pyramid:
V_total = V_rectangular prism + V_pyramid
V_total = 24 ft³ + 6 ft³
V_total = 30 ft³
Therefore, the corrected volume of the dollhouse is 30 cubic feet.