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