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3 years ago

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A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius o

f the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 3 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 22,500 cubic feet of grain?

2 answers:

mezya [45]3 years ago

7 0

Answer:

10.24 ft

Step-by-step explanation:

Aleks04 [339]3 years ago

4 0

Answer:

about 10.24 ft

Step-by-step explanation:

The formula for the volume of a cylinder is ...

V = πr²h . . . . where h is the height and r is the radius

The formula for the volume of a sphere is ...

V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r

__

We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.

Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...

22,500 ft³ = πr²·(20/3)r = (20π/3)r³

Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...

r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft

The radius of the silo should be about 10.24 feet.

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