Question

a wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid. the dimensions of the prism are 23 ft by 23 ft by 9 ft, and the height of the pyramid is 2 ft. find the total volume of the tent. round your answer to the nearest tenth if necessary. (note: diagram is not drawn to scale.)

Explanation:

Step1: Calculate the volume of the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 23\) ft, \(w = 23\) ft, \(h = 9\) ft.
\(V_{prism}=23\times23\times9=23^{2}\times9 = 529\times9=4761\) cubic feet.

Step2: Calculate the volume of the rectangular pyramid

The volume formula for a rectangular pyramid is \(V=\frac{1}{3}\times B\times h\), where \(B\) is the base area. The base of the pyramid is the same as the base of the prism, so \(B = 23\times23 = 529\) square feet and \(h = 2\) ft.
\(V_{pyramid}=\frac{1}{3}\times529\times2=\frac{1058}{3}\approx352.7\) cubic feet.

Step3: Calculate the total volume

The total volume \(V = V_{prism}+V_{pyramid}\).
\(V=4761 + 352.7=5113.7\) cubic feet.

Answer:

\(5113.7\) cubic feet.