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 33 ft by 35 ft by 10 ft, and the height of the pyramid is 4 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 \(V_{prism}=l\times w\times h\). Here, \(l = 35\) ft, \(w = 33\) ft, \(h = 10\) ft.
\(V_{prism}=35\times33\times10= 11550\) \(ft^{3}\)

Step2: Calculate the volume of the rectangular pyramid

The volume formula for a rectangular pyramid is \(V_{pyramid}=\frac{1}{3}\times B\times h\), where \(B\) is the base area. The base of the pyramid has the same length and width as the prism, so \(B = 35\times33\). The height of the pyramid \(h = 4\) ft.
\(V_{pyramid}=\frac{1}{3}\times35\times33\times4=\frac{4620}{3}=1540\) \(ft^{3}\)

Step3: Calculate the total volume

The total volume \(V = V_{prism}+V_{pyramid}\)
\(V=11550 + 1540=13090\) \(ft^{3}\)

Answer:

\(13090\) \(ft^{3}\)