Acompany 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(2ft)2(10ft) + one over threeπ(13ft − 10ft)2(2ft)
b.) π(10ft)2(2ft) + one over threeπ(13ft − 10ft)2(2ft)
c.) π(2ft)2(10ft) + one over threeπ(2ft)2(13ft − 10ft)
d.) π(10ft)2(2ft) + one over threeπ(2ft)2(13ft − 10ft)

C.) π(2ft)²(10ft) + one over three π(2ft)²(13ft − 10ft)

Step-by-step explanation:

We basically have here 2 volumes to calculate, the one of a cylinder (radius: 2 ft, height 10 ft) and one of a cone (radius 2ft, height 3 ft).

To calculate the volume of a cylinder, the formula is:

V = π r² h, which in our case is π(2ft)²(10ft)

To calculate the volume of a cone, the formula is:

V = (1/3) π r² h, which in our case is (1/3) π(2ft)²(13ft − 10ft)

So, to have the total volume, you need to add them together:

V = π(2ft)²(10ft) +  (1/3) π(2ft)²(13ft − 10ft)

Which is answer C (if we correct the exponents).

The correct answer is

C.)

Step-by-step explanation:

We can divide the total volume of the silo into two :

A cylinder with a radius of 2 ft and height 10 ft

And a cone with a radius of 2 ft and height 3 ft

The volume of a cylinder with radius R and height H is :

The volume of a cone with radius R and height H is :

In the exercise, the volume of the cylinder with radius 2 ft and height 10 ft is :

The volume of the cone with radius 2 ft and height 3 ft is :

Rearranging the expression :

In the expression, we write the height of the cone as the difference between 13 ft and 10 ft

The correct option is option C.)

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