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 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, and \( h \) is the height.
Given:
- Volume \( V = 600,000 \, \text{cm}^3 \)
- Height \( h = 76 \, \text{cm} \)
We need to solve for \( r \). Rearranging the formula gives us:
\[
r^2 = \frac{V}{\pi h}
\]
Substituting the known values:
\[
r^2 = \frac{600,000}{\pi \times 76}
\]
Calculating \( \pi \times 76 \):
\[
\pi \times 76 \approx 238.76
\]
Now substituting that into the equation:
\[
r^2 = \frac{600,000}{238.76} \approx 2511.47
\]
Taking the square root to find \( r \):
\[
r = \sqrt{2511.47} \approx 50.11
\]
Rounding to the nearest whole number, we find:
\[
r \approx 50 \, \text{cm}
\]
Thus, the radius is approximately **50 cm**.
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Volume \( V = 600,000 \, \text{cm}^3 \)
- Height \( h = 76 \, \text{cm} \)
We need to solve for \( r \). Rearranging the formula gives us:
\[
r^2 = \frac{V}{\pi h}
\]
Substituting the known values:
\[
r^2 = \frac{600,000}{\pi \times 76}
\]
Calculating \( \pi \times 76 \):
\[
\pi \times 76 \approx 238.76
\]
Now substituting that into the equation:
\[
r^2 = \frac{600,000}{238.76} \approx 2511.47
\]
Taking the square root to find \( r \):
\[
r = \sqrt{2511.47} \approx 50.11
\]
Rounding to the nearest whole number, we find:
\[
r \approx 50 \, \text{cm}
\]
Thus, the radius is approximately **50 cm**.