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What is the volume of the greenhouse?
JMAP geometry math prism cylinder
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The greenhouse pictured below can be modeled as a rectangular prism with a half-cylinder on top. The rectangular prism is 20 feet wide, 12 feet high, and 45 feet long. The half-cylinder has a diameter of 20 feet.

To the nearest cubic foot, what is the volume of the greenhouse?

1) 17,869

3) 39,074

2) 24,937

4) 67,349

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judziy
Asked by judziyrep:876
University of Benin Nigeria
23 June 2020

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peter
Peter answeredrep:907
University of Lagos Nigeria
12 August 2020
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Since the greenhouse comprises of a rectangular prism and half a cylinder, the volume of the railing = volume of rectangular prism + half the volume of a cylinder.

Volume of rectangular prism = L x H x W.

Where H is the height of the rectangular section of the greenhouse, H is the height of the rectangular section of the greenhouse and W is the width of the rectangular section of the greenhouse.

Thus, volume of the rectangular section of the greenhouse = 45 x 20 x 12

= 10,800

Volume of cylinder = πr2h. Where r is the radius and h is the height.

radius = diameter/2 = 20/2 = 10

volume of the cylindrical section = π x (10)2 x 45

= 4500π

Thus, half the volume = 4500π/2

= 2250π

Therefore, the total volume = 10800 + 2250π

= 17,869

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