Find the volume specified. Use 3.14 as the approximate value of , and round your answer to the nearest tenth.
Find the volume of a tent having the shape of a rectangular solid of length 12 ft, width 12 ft, and height 6 ft topped by a rectangular pyramid of the same width and length with height
5 ft
To find the volume of the tent, we need to find the volume of the rectangular solid and the volume of the pyramid and then add them together.
The volume of a rectangular solid is given by:
Volume = length * width * height
Plugging in the given values, we have:
Volume of rectangular solid = 12 ft * 12 ft * 6 ft = 864 ft^3
The volume of a pyramid is given by:
Volume = (1/3) * base area * height
Since the base of the pyramid is a rectangle with the same width and length as the rectangular solid, the base area is given by:
Base area = length * width
Plugging in the given values, we have:
Base area = 12 ft * 12 ft = 144 ft^2
Now, we can calculate the volume of the pyramid:
Volume of pyramid = (1/3) * 144 ft^2 * 5 ft = 240 ft^3
Finally, we add the volumes together:
Total volume = Volume of rectangular solid + Volume of pyramid
Total volume = 864 ft^3 + 240 ft^3 = 1104 ft^3
Rounding to the nearest tenth, the volume of the tent is approximately 1104 ft^3.