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.)

entering that problem on the tube might get you an answer