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A wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid. The dimensions of the prism are 32 ft by 35 ft by 9 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.)

A wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid The dimensions of the prism are 32 ft by 35 ft by 9 ft and t class=

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Answer:

11573.3 cubic feet

Explanations:

The given tent is made up of a rectangular pyramid and prism. The formula for calculating the volume of the tent is expressed as:

[tex]V=volume\text{ of pyramid + volume of prism}[/tex]

Find the volume of the prism

[tex]\begin{gathered} Vol.\text{ of prism}=Base\text{ area }\times Height \\ Vol.\text{ of prism}=(35\times32)\times9 \\ Vol.\text{ of prism}=1120\times9 \\ Vol.\text{ of prism}=10,080ft^3 \end{gathered}[/tex]

Find the volume of the topped pyramid

[tex]\begin{gathered} Vol.\text{ of pyramid}=\frac{BH}{3} \\ Vol.\text{ of pyramid}=\frac{(35\times32)\times4}{3} \\ Vol.\text{ of pyramid}=\frac{4480}{3} \\ Vol.\text{ of pyramid}=1493.3ft^3 \end{gathered}[/tex]

Determine the area of the tent

[tex]\begin{gathered} volume\text{ of tent}=10,080+1493.3 \\ volume\text{ of tent}=11573.3ft^3 \end{gathered}[/tex]

Therefore the total volume of the tent to the nearest tenth is 11573.3 cubic feet

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