To find the radius of the cylinder given its volume and height, we need to use the formula for the volume of a cylinder, which is:
[tex]\[ V = \pi r^2 h \][/tex]
Given:
- Volume [tex]\( V = 8,792 \)[/tex] cubic units
- Height [tex]\( h = 7 \)[/tex] units
We are asked to find the radius [tex]\( r \)[/tex].
1. First, we rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r^2 = \frac{V}{\pi h} \][/tex]
2. Substitute the given values for [tex]\( V \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ r^2 = \frac{8,792}{\pi \times 7} \][/tex]
3. Calculate the value inside the fraction:
[tex]\[ \pi \approx 3.14159 \][/tex]
[tex]\[ r^2 = \frac{8,792}{3.14159 \times 7} \][/tex]
[tex]\[ r^2 = \frac{8,792}{21.99113} \][/tex]
[tex]\[ r^2 = 399.96883 \][/tex]
4. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{399.96883} \][/tex]
[tex]\[ r \approx 20 \][/tex]
Given the options:
- A. 10 units
- B. 20 units
- C. 40 units
- D. 15 units
The radius of the cylinder is approximately 20 units. Therefore, the correct answer is:
[tex]\[ \boxed{20 \text{ units}} \][/tex]
