To determine the radius of a sphere given its volume, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the sphere
- [tex]\( r \)[/tex] is the radius of the sphere
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159
Given:
[tex]\[ V = 904.78 \, \text{m}^3 \][/tex]
We need to solve for [tex]\( r \)[/tex]. First, we rearrange the equation to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \][/tex]
Substitute the given volume into the equation:
[tex]\[ r = \left( \frac{3 \cdot 904.78}{4 \cdot \pi} \right)^{\frac{1}{3}} \][/tex]
Perform the calculations step-by-step:
1. Multiply the volume by 3:
[tex]\[ 3 \cdot 904.78 = 2714.34 \][/tex]
2. Multiply [tex]\( \pi \)[/tex] by 4:
[tex]\[ 4 \cdot \pi \approx 4 \cdot 3.14159 = 12.56636 \][/tex]
3. Divide the result from step 1 by the result from step 2:
[tex]\[ \frac{2714.34}{12.56636} \approx 216.0635 \][/tex]
4. Take the cube root of the result from step 3:
[tex]\[ \left( 216.0635 \right)^{\frac{1}{3}} \approx 6 \][/tex]
Thus, the radius [tex]\( r \)[/tex] calculated is very close to 6 meters.
Given the options:
- 29.4 m
- 06 m
- 12 m
- 14.7 m
- None of the other answers are correct
The closest value to our calculated radius of approximately 6 meters is indeed 06 m.
Therefore, the correct answer is:
[tex]\[ 06 \, \text{m} \][/tex]
