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.
Answers
GPT-4o mini
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.
Given:
- \( V = 600,000 \) cm³
- \( h = 76 \) cm
We can rearrange the formula to solve for \( r \):
\[
r^2 = \frac{V}{\pi h}
\]
Substituting in the known values:
\[
r^2 = \frac{600,000}{\pi \times 76}
\]
Now calculate \( \pi \times 76 \):
\[
\pi \approx 3.14159 \implies \pi \times 76 \approx 238.76
\]
Now calculate \( \frac{600,000}{238.76} \):
\[
r^2 \approx \frac{600,000}{238.76} \approx 2512.42
\]
Now, take the square root of that to find the radius \( r \):
\[
r \approx \sqrt{2512.42} \approx 50.12
\]
Rounding to the nearest whole number, the radius of the container is approximately:
\[
\boxed{50} \text{ cm}
\]
\[
V = \pi r^2 h
\]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given:
- \( V = 600,000 \) cm³
- \( h = 76 \) cm
We can rearrange the formula to solve for \( r \):
\[
r^2 = \frac{V}{\pi h}
\]
Substituting in the known values:
\[
r^2 = \frac{600,000}{\pi \times 76}
\]
Now calculate \( \pi \times 76 \):
\[
\pi \approx 3.14159 \implies \pi \times 76 \approx 238.76
\]
Now calculate \( \frac{600,000}{238.76} \):
\[
r^2 \approx \frac{600,000}{238.76} \approx 2512.42
\]
Now, take the square root of that to find the radius \( r \):
\[
r \approx \sqrt{2512.42} \approx 50.12
\]
Rounding to the nearest whole number, the radius of the container is approximately:
\[
\boxed{50} \text{ cm}
\]