Question

549.5 cubic inches in volume is 7 inches tall. What is the radius of the cylinder?
Use 3.14 for π.

Answer 1

To find the radius of a cylinder given its volume and height, 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,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.

Given:
- \( V = 549.5 \) cubic inches,
- \( h = 7 \) inches,
- \( \pi \approx 3.14 \).

We can rearrange the formula to solve for the radius \( r \):

\[
r^2 = \frac{V}{\pi h}
\]

Now we can substitute the known values into this rearranged formula:

\[
r^2 = \frac{549.5}{3.14 \times 7}
\]

Calculating the denominator:

\[
3.14 \times 7 = 21.98
\]

Now substituting back the values:

\[
r^2 = \frac{549.5}{21.98} \approx 24.98
\]

Now, to find \( r \), we take the square root of both sides:

\[
r \approx \sqrt{24.98} \approx 5
\]

Thus, the radius of the cylinder is approximately:

\[
\boxed{5} \text{ inches}
\]