Question

What is the diameter of a sphere if the volume is 50965 units cubed ?

Answer 1

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:

1. Calculate \( 3 \times 50965 = 152895 \).
2. Approximate \( \pi \) as \( 3.14159 \).
3. Calculate \( 4\pi \approx 12.56636 \).
4. Now calculate \( r^3 \):

\[
r^3 = \frac{152895}{12.56636} \approx 12104.7
\]

5. Now, find \( r \) by taking the cube root:

\[
r \approx \sqrt[3]{12104.7} \approx 22.9 \text{ units}
\]

6. 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**.