Find the volume specified. Use 3.14 as the approximate value of pie, and round your answer to the nearest tenth
Find the volume of a tent having the shape of a rectangular solid of length 10 ft, width 15 ft, and height 9 ft topped by a rectangular pyramid of the same width and length with height
7ft
The volume of the rectangular solid can be found by multiplying the length, width, and height:
Volume of rectangular solid = length * width * height
= 10 ft * 15 ft * 9 ft
= 1350 ft^3
To find the volume of the rectangular pyramid, we need to find the area of the base first. The base is a rectangle with a length of 15 ft and a width of 10 ft. Therefore, the area of the base is:
Area of base = length * width
= 15 ft * 10 ft
= 150 ft^2
Then, we can find the volume of the pyramid using the formula:
Volume of pyramid = (1/3) * base area * height of pyramid
= (1/3) * 150 ft^2 * 7 ft
= 350 ft^3
Finally, to find the total volume of the tent, we add the volume of the rectangular solid and the volume of the pyramid together:
Total volume = volume of rectangular solid + volume of pyramid
= 1350 ft^3 + 350 ft^3
= 1700 ft^3
Rounded to the nearest tenth, the volume of the tent is 1700 ft^3.