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A grain silo is in the shape of a cylinder. The silo has a diameter of 12 feet and a height of 20 feet.Part A: How many cubic feet of grain can fit into this silo? Use 3.14 for pi.Part B: Famer Tom purchases bags of grain to fill the silo. If each bag fills 12 cubic feet of the silo with grain, how many bags must Farmer Tom purchase to completely fill the silo? Explain, or show your work.

Respuesta :

Given:

Cylinder

Diameter: 12ft

Height: 20ft

Part A: Find the volume of the silo

Volume of a cylinder:

[tex]V=h\cdot\pi\cdot r^2[/tex]

r is the radius (radius is half of the diameter)

h is the height

[tex]\begin{gathered} V=20ft\cdot3.14\cdot(\frac{12ft}{2})^2 \\ \\ V=20ft\cdot3.14\cdot(6ft)^2 \\ \\ V=20ft\cdot3.14\cdot36ft^2 \\ \\ V=2260.8ft^3 \end{gathered}[/tex]

Then, in the silo can fit 2260.8 cubic feet of grain

Part B: As each bag fills 12 cubic feet, divide the number of cubic feet that can fit in the silo into 12 to find the total number of bags that the farmer must purchase:

[tex]\frac{2260.8}{12}=\frac{22608}{120}[/tex]

Then, the farmer needs to purchase 188.4 (or 189 whole number of bags) bags to completely fill the silo

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