To find the radius and diameter of the cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) = volume of the cylinder
- \( r \) = radius
- \( h \) = height
- \( \pi \) is approximated as 3.14.
Given:
- \( V = 502.4 , \text{m}^3 \)
- \( h = 10 , \text{m} \)
We can rearrange the volume formula to solve for the radius \( r \):
\[ r^2 = \frac{V}{\pi h} \]
Substituting the known values:
\[ r^2 = \frac{502.4}{3.14 \times 10} \] \[ r^2 = \frac{502.4}{31.4} \] \[ r^2 = 16 \]
Now, taking the square root of both sides:
\[ r = 4 , \text{m} \]
Now, we can find the diameter \( d \) using the formula:
\[ d = 2r \] \[ d = 2 \times 4 , \text{m} = 8 , \text{m} \]
Now we can examine the answer choices:
A. radius = 4 m ✅
B. radius = 16 m
C. diameter = 32 m
D. diameter = 2 m
E. diameter = 8 m ✅
The correct statements are:
- A: radius = 4 m
- E: diameter = 8 m
So the two correct statements are A and E.