Question

B) What is the diameter if the volume is 50965 units \(^3\)? (1 point)
sphere

Answer 1

To find the diameter of a sphere given its volume, you 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. We can rearrange this formula to solve for the radius:

\[
r^3 = \frac{3V}{4\pi}
\]

\[
r = \sqrt[3]{\frac{3V}{4\pi}}
\]

Once we find the radius, we can determine the diameter \( d \) using the relationship:

\[
d = 2r
\]

Now, substituting the given volume \( V = 50965 \) units\(^3\):

1. Calculate \( r \):

\[
r = \sqrt[3]{\frac{3 \times 50965}{4 \pi}}
\]

Calculating this step-by-step:

1. Calculate \( 4\pi \):

\[
4 \pi \approx 12.5664
\]

2. Calculate \( 3 \times 50965 \):

\[
3 \times 50965 = 152895
\]

3. Now substitute into the formula for \( r \):

\[
r = \sqrt[3]{\frac{152895}{12.5664}} \approx \sqrt[3]{12104.746} \approx 22.96
\]

4. Now calculate the diameter \( d \):

\[
d = 2r \approx 2 \times 22.96 \approx 45.92
\]

Thus, the diameter of the sphere is approximately **45.92 units**.