A wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid. The dimensions of the prism are 30 ft by 36 ft by 8 ft, and the height of the pyramid is 5 ft. Find the total volume of the tent. Round your answer to the nearest tenth if necessary

Respuesta :

The total volume of the tent to the nearest tenth is 10440.0 ft³

Volume of rectangular prism

  • v = lwh

where

l  = length

w = width

h = height

Therefore,

volume of the rectangular prism = 30 × 36 × 8

volume of the rectangular prism = 8640 ft³

Volume of the rectangular pyramid

  • v = [tex]\frac{1}{3} Bh[/tex]

where

B = base area

h = height

h = 5 ft

B = 30 × 36 = 1080 ft²

v = [tex]\frac{1}{3} (1080)(5)[/tex]

v = [tex]\frac{5400}{3}[/tex]

v = 1800 ft³

Therefore, the volume of the whole tent is calculated as follows:

v = 1800 + 8640 = 10440 ft³

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