The volume of a right circular cylinder is equal to its height (\(\displaystyle h\)) multiplied by the area of the circle base (\(\displaystyle \pi r^2\)).

In this scenario, the Volume

\(\displaystyle V=5* (\pi *3^2) = 45\pi\).

Therefore, the volume is \(\displaystyle 45\pi\).

Plug the radius and height into the formula for the volume of a cylinder:
\(\displaystyle \\V = \pi *r^2*h \newline V = \pi * 4^2 * 7 \newline V = 112 \pi inches^3\)

To find the volume of a cylinder use formula:

\(\displaystyle V = \pi r^2*h\)

For a cylinder with a radius of 6 and a height of 3 this yields:

\(\displaystyle V = \pi 6^2*3\)

     \(\displaystyle =108\pi\)

To find volume, simply use the following formula. Remember, you were given diameter so radius is half of that. Thus,

\(\displaystyle V=\pi{r^2}h=\pi*3^2*8=72\pi\)

To find volume of a cylinder, simply use the following formula. Thus,

\(\displaystyle \textup{volume}=\pi{r^2}h=\pi*(3^2)*2=\pi*9*2=18\pi\)

To solve, simply use the formula. Thus,

\(\displaystyle V=\pi{r^2}h=\pi\cdot1^2\cdot11=\pi\cdot1\cdot11=11\pi\)

To solve, simply use the formula for volume of a cylinder.

First, identify what is known.

Height = 1

Radius = 1

Substitute these values into the formula and solve.

Thus,

\(\displaystyle V=\pi{r^2}h=\pi*1^2*1=\pi\)

To solve, simply use the following formula. Thus,

\(\displaystyle V=\pi{r^2}h=\pi*2^2*8=\pi*4*8=32\pi\)

The volume of a cylinder is found using the following formula:

\(\displaystyle V = \pi r^2 h\)

In this formula, the variable \(\displaystyle h\) is the height of the cylinder and \(\displaystyle r\) is its radius. Since the diameter is two times the radius, first solve for the radius. 

\(\displaystyle \text{Diameter}=2r\)

\(\displaystyle 18=2r\)

Divide both sides of the equation by 2.

\(\displaystyle \frac{18}{2}=\frac{2r}{}2\)

\(\displaystyle r=9\)

The given cylinder has a radius of 9 feet. Now, substitute the calculated and known values into the equation for the volume of a cylinder and solve.

\(\displaystyle V=\pi\times9^{2}\times 100\)

\(\displaystyle V=8100\pi\)

This is the total volume of the tank. The question asks for the volume of ten percent of the tank—the point at which the filter must be replaced. To find this, move the decimal point in the numerical measure of total volume to the left one place in order to calculate ten percent of the total volume. (Ignore \(\displaystyle \pi\)—you can treat it like a multiplier here. Since it appears on both sides of the equals sign, it doesn't affect the decimal shift.)

\(\displaystyle 8100\pi\times 0.10=810\pi\)

The tank can hold \(\displaystyle 810\pi\) cubic feet of sediment before the filter needs to be changed.

SA_cylinder = 2πrh + 2πr² = 2π(2)(10) + 2π(2)² = 40π + 8π = 48π cm²