Question

This sphere has a diameter of 5 m.

A sphere with diameter 5 meters.

What is the volume of the sphere?
V = StartFraction 9 Over 2 EndFraction pim3
V = StartFraction 125 Over 6 Endfraction pim3
V = StartFraction 500 Over 3 EndFraction pim3
V = StartFraction 4,000 Over 3 EndFractionm3

Answer 1

To calculate the volume of a sphere, you can use the formula:

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

where \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 5 meters, the radius \( r \) is half of the diameter:

\[
r = \frac{5}{2} = 2.5 \text{ m}
\]

Now, substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (2.5)^3
\]

First, calculate \( (2.5)^3 \):

\[
(2.5)^3 = 2.5 \times 2.5 \times 2.5 = 6.25 \times 2.5 = 15.625
\]

Now substitute that back into the volume formula:

\[
V = \frac{4}{3} \pi \times 15.625
\]

Now multiply:

\[
V = \frac{4 \times 15.625}{3} \pi = \frac{62.5}{3} \pi \text{ m}^3
\]

Thus, the volume of the sphere is

\[
V = \frac{62.5}{3} \pi \text{ m}^3
\]

Now, let's simplify \( \frac{62.5}{3} \):

\[
\frac{62.5}{3} = \frac{125}{6}
\]

Therefore, the volume of the sphere can be expressed as:

\[
V = \frac{125}{6} \pi \text{ m}^3
\]

So the correct option is:

\[
V = \frac{125}{6} \pi \text{ m}^3
\]