Question

502.4 cubic centimeters in volume has a radius of 4 centimeters. What is the height of the cylinder?
Use 3.14 for π.

Answer 1

To find the height of a cylinder when you know its volume and radius, you 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.

Given:
- \( V = 502.4 \) cubic centimeters,
- \( r = 4 \) centimeters, and
- \( \pi = 3.14 \).

Substituting the values into the formula:

\[
502.4 = 3.14 \times (4^2) \times h
\]

Calculating \( 4^2 \):

\[
4^2 = 16
\]

Now substitute \( 16 \) back into the equation:

\[
502.4 = 3.14 \times 16 \times h
\]

Calculating \( 3.14 \times 16 \):

\[
3.14 \times 16 = 50.24
\]

So the equation becomes:

\[
502.4 = 50.24 \times h
\]

Now, solve for \( h \) by dividing both sides by \( 50.24 \):

\[
h = \frac{502.4}{50.24}
\]

Calculating the right side:

\[
h \approx 10
\]

Thus, the height of the cylinder is approximately \( 10 \) centimeters.