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 . Round your answer to the nearest whole number.(1 point)
The radius is about
cm.

Answer 1

To find the radius of the cylindrical recycling container, 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, and
- \( \pi \) is a constant approximately equal to 3.14159.

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

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

Given:
- Volume \( V = 600,000 \, \text{cm}^3 \)
- Height \( h = 76 \, \text{cm} \)

Now substitute the values into the equation:

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

First, calculate \( \pi \times 76 \):

\[
\pi \times 76 \approx 3.14159 \times 76 \approx 238.76164
\]

Next, calculate \( \frac{600,000}{238.76164} \):

\[
\frac{600,000}{238.76164} \approx 2512.566
\]

Now take the square root:

\[
r \approx \sqrt{2512.566} \approx 50.12
\]

Rounding to the nearest whole number, the radius \( r \) is approximately:

\[
\boxed{50} \, \text{cm}
\]