Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the two bases:

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

For our problem, this is:

Therefore, the total surface area is:

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the two bases:

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

For our problem, this is:

Therefore, the total surface area is:

To calculate the volume, you must plug into the formula given in the problem. When you plug in, it should look like this: . Multiply all of these out and you get . The units are cubed because volume is always cubed.

To calculate the volume, you must plug into the formula given in the problem. When you plug in, it should look like this: . Multiply all of these out and you get . The units are cubed because volume is always cubed.

Your family owns a farm with a silo for storing grain. If the silo is 40 feet tall and 15 feet in diameter, what volume of grain can it hold?

Begin with the formula for volume of a cylinder.

A cylinder is just a circle with height.

So, we know the height is 40 ft, but what is r?

If you said 15, you would be on track to get the problem wrong. That is because the diameter is 15 ft, so our radius is only 7.5 ft.

Plug these in to get our answer:

Our answer should be

Your family owns a farm with a silo for storing grain. If the silo is 40 feet tall and 15 feet in diameter, what volume of grain can it hold?

Begin with the formula for volume of a cylinder.

A cylinder is just a circle with height.

So, we know the height is 40 ft, but what is r?

If you said 15, you would be on track to get the problem wrong. That is because the diameter is 15 ft, so our radius is only 7.5 ft.

Plug these in to get our answer:

Our answer should be

Recall that the equation of for the volume of a cylinder is:

For our values this is:

Solve for :

Using a calculator to calculate , you will see that

To find the volume of a cylinder, we will use the following formula:

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We also know the height of the cylinder is 7in.

Knowing all of this, we can substitute into the formula. We get

To find the volume of a cylinder, we will use the following formula:

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We also know the height of the cylinder is 7in.

Knowing all of this, we can substitute into the formula. We get

Recall that the equation of for the volume of a cylinder is:

For our values this is:

Solve for :

Using a calculator to calculate , you will see that