To find the diameter of a sphere given its volume, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere. Given that the volume \( V = 50965 \) cubic units, we can rearrange the formula to solve for the radius:
\[ r^3 = \frac{3V}{4\pi} \]
Substituting in the value of \( V \):
\[ r^3 = \frac{3 \times 50965}{4\pi} \]
Calculating this step-by-step:
- Calculate \( 3 \times 50965 = 152895 \).
- Approximate \( \pi \) as \( 3.14159 \).
- Calculate \( 4\pi \approx 12.56636 \).
- Now calculate \( r^3 \):
\[ r^3 = \frac{152895}{12.56636} \approx 12104.7 \]
- Now, find \( r \) by taking the cube root:
\[ r \approx \sqrt[3]{12104.7} \approx 22.9 \text{ units} \]
- Finally, the diameter \( d \) of the sphere is twice the radius:
\[ d = 2r \approx 2 \times 22.9 \approx 45.8 \text{ units} \]
Thus, the diameter of the sphere is approximately 45.8 units.