Write the formula for the volume of the cylinder.

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

The height is 14, since it is twice the radius.  Substitute the dimensions.

\(\displaystyle \\V=\pi (7)^2 (14 ) \\V=\pi 49\cdot 14\\ V=686 \pi\)

Write the formula for the volume of a cylinder.

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

The radius is unknown.  In order to solve for the radius, use the base perimeter as a given to solve for the radius.  The base perimeter is the circular circumference.

Write the formula for the circle's circumference.

\(\displaystyle C=2\pi r\)

Substitute the base perimeter.

\(\displaystyle 6\pi=2\pi r\)

Divide \(\displaystyle 2\pi\) on both sides to solve for the radius.

\(\displaystyle \frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}\)

\(\displaystyle r=3\)

Substitute the radius and the height into the volume formula.

\(\displaystyle V=\pi r^2h = \pi (3)^2 (6) = \pi (9)(6) =54\pi\)

The formula to find the volume of a cylinder is

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

We know the diameter of the cylinder is 4in.  The radius is half the diameter, so the radius of the cylinder is 2in.  We know,

\(\displaystyle \pi = 3.14\)

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

\(\displaystyle h = 5 \text{in}\)

When we substitute into the formula, we get

\(\displaystyle V = 3.14 * (2\text{in})^2 * 5\text{in}\)

\(\displaystyle V = 3.14 * 4\text{in}^2 * 5\text{in}\)

\(\displaystyle V = 62.8\text{in}^3\)

Therefore, the volume of the soup can is \(\displaystyle 62.8\text{in}^3\)

The formula for the volume of a cylinder is:

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

To find the radius, we simply plug in the given values and solve for \(\displaystyle r\):

\(\displaystyle 288\pi =\pi r^2(8)\)

\(\displaystyle \frac{288\pi}{\pi} =\frac{8\pi r^2}{\pi}\)

\(\displaystyle 288=8r^2\)

\(\displaystyle \frac{288}{8}=\frac{8r^2}{8}\)

\(\displaystyle 36=r^2\)

\(\displaystyle \sqrt{36}=\sqrt{r^2}\)

\(\displaystyle 6=r\)

Therefore, the radius of the circle is \(\displaystyle 6\).

To find the volume of a cylinder, the formula is \(\displaystyle V = \pi r^{2} h\).
Normally, you would simply input the radius given for "\(\displaystyle r\)" and the height given for "\(\displaystyle h\)". However, the question did not directly give us the radius; it gave us the area of the circular bottom. 

Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If \(\displaystyle \pi r^{2}\) is the area of a circle, then we can simply multiply the area of the circle given by the height given.

V = area of the circle x height
\(\displaystyle V=10\pi \times 8\)
\(\displaystyle V=80\pi\) cubed inches

The base of a cylinder is a circle.  Write the circumference formula.

\(\displaystyle C=2\pi r\)

Substitute the circumference and find the radius.

\(\displaystyle 4\pi=2\pi r\)

\(\displaystyle r=2\)

Write the formula to find the volume for cylinders.

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

Substitute the dimensions.

\(\displaystyle V=\pi (2)^2 (4) = 16\pi\)

If the box is 4 inches tall, then its height is 4in.  Since the width is twice the height, the width must be 8 inches.  Since the length is three times the width, the length must be 24 inches.  Since a rectangular box is just a rectangular solid, the formula for the volume of a rectangular solid will give us the volume of the Trayvon's box.

\(\displaystyle V=lwh\), where \(\displaystyle l\) is length, \(\displaystyle w\) is width, and \(\displaystyle h\) is height.  Therefore,

\(\displaystyle V=(24)(8)(4)=768\)

Since the unit of each of our dimensions was inches, our volume will be in cubic inches.  Thus our answer is \(\displaystyle 768in.^{3}\)

Divide each dimension in inches by 12 to convert from inches to feet:

\(\displaystyle L = 24 \div 12 = 2\) feet

\(\displaystyle W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}\) feet

\(\displaystyle H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}\) feet

Multiply the three to get the volume:

\(\displaystyle V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}\) cubic feet

In order to figure out how many cubic centimeters can fit into the box, we need to figure out the volume of the box in terms of cubic centimeters. However, the measurements of the box are given in meters. Therefore, we need to convert these measurements to centimeters and then determine the volume of the box.

There are 100 centimeters in one meter. This means that in order to convert from meters to centimeters, we must multiply by 100.

The length of the box is 2 meters, which is equal to 2 x 100, or 200, centimeters.

The width of the box is 0.5(100) = 50 centimeters.

The height of the box is 3.2(100) = 320 centimeters.

Now that all of our measurements are in centimeters, we can calculate the volume of the box in cubic centimeters. Remember that the volume of a rectangular box (or prism) is equal to the product of the length, width, and height.

V = length x width x height

V = (200 cm)(50 cm)(320 cm) = 3,200,000 cm³

To rewrite this in scientific notation, we must move the decimal six places to the left.

V = 3.2 x 10⁶ cm³

The answer is 3.2 x 10⁶.

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla \(\displaystyle v=l\cdot w\cdot h\).  Since a cube has equal sides, we can use \(\displaystyle 8\) for all three values.

\(\displaystyle 8\cdot 8\cdot 8=512\: in ^{3}\)