A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:

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Question:

A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:Which of the following could be used to calculate the total volume of grains that can be stored in the silo?
A. π(8.5ft)2(2ft) + one over three π(2ft)2(13ft − 8.5ft)
B. π(2ft)2(8.5ft) + one over three π(2ft)2(13ft − 8.5ft)
C. π(8.5ft)2(2ft) + one over three π(13ft − 8.5ft)2(2ft)
D. π(2ft)2(8.5ft) + one over threeπ(13ft − 8.5ft)2(2ft)

Answer:

Option B is correct.

The storage bin is constructed using a cylinder and a cone. Hence the total volume of the grain can be calculated using the formula;

Vc is the volume of the cylinder

Vco is the volume of the cone.

For the cylinder:

Height of the cylinder hc = 8.5ft

radius rc = 4/2 = 2ft

For the cone:

Height of the cone = (13 – 8.5)ft

radius of the cone = radius of the cylinder rco = 2ft

Taking the sum of the volumes;

This shows that option B is correct.

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