The cylinder shown has a radius of 7 millimeters (mm) and a volume of 441π mm3 . What is the height of the cylinder? Show your work.

Answer 1

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

From the problem, we know:

• The radius \( r = 7 \) mm
• The volume \( V = 441\pi \) mm\(^3\)

We can substitute these values into the volume formula:

\[ 441\pi = \pi (7^2) h \]

First, calculate \( 7^2 \):

\[ 7^2 = 49 \]

Now, substitute that into the equation:

\[ 441\pi = \pi (49) h \]

Next, we can divide both sides of the equation by \( \pi \) (assuming \( \pi \neq 0 \)) to simplify:

\[ 441 = 49h \]

Now, solve for \( h \) by dividing both sides by 49:

\[ h = \frac{441}{49} \]

Calculating that gives:

\[ h = 9 \]

Thus, the height of the cylinder is

\[ \boxed{9} \text{ mm}. \]

Answer 2

try again

Answer 3

Let's solve the problem step by step again.

We know the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where:

• \( V \) is the volume,
• \( r \) is the radius,
• \( h \) is the height.

From the problem, we have:

• Volume \( V = 441\pi \) mm\(^3\)
• Radius \( r = 7 \) mm

Now, let's substitute the known values into the volume formula:

\[ 441\pi = \pi (7^2) h \]

Calculate \( 7^2 \):

\[ 7^2 = 49 \]

Now, substitute that back into the volume formula:

\[ 441\pi = \pi (49) h \]

Next, we can divide both sides by \( \pi \) (again, assuming \( \pi \neq 0 \)):

\[ 441 = 49h \]

Now we solve for \( h \):

\[ h = \frac{441}{49} \]

Since \( 441 \div 49 = 9 \), we get:

\[ h = 9 \]

Thus, the height of the cylinder is

\[ \boxed{9} \text{ mm}. \]

Please let me know if there's anything specific you would like me to clarify or if there's a different aspect of the problem you believe needs reconsideration!