Question

A cylindrical recycling container has a height of 76 centimeters, but the radius is unknown. Find the radius if the container has a volume of 600,000 cm3
600
,
000

cm
3
. Round your answer to the nearest whole number.

Answer 1

To find the radius of a cylindrical recycling container 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.

We know:
- \( V = 600,000 \) cm³
- \( h = 76 \) cm

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

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

Substituting in the known values:

\[
r^2 = \frac{600,000}{\pi \times 76}
\]

Calculating \( \pi \times 76 \):

\[
\pi \times 76 \approx 238.76
\]

Now plug this into the equation:

\[
r^2 = \frac{600,000}{238.76}
\]

Calculating \( \frac{600,000}{238.76} \):

\[
r^2 \approx 2510.84
\]

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

\[
r \approx \sqrt{2510.84} \approx 50.1
\]

Rounding to the nearest whole number, we find:

\[
r \approx 50 \text{ cm}
\]

Thus, the radius of the container is approximately **50 cm**.