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.