Question

A ball shaped like a sphere has a radius of 3.7 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters?
Responses
A 212.17 cm³212.17 cm³
B 113.10 cm³113.10 cm³
C 33.51 cm³33.51 cm³
D 210.17 cm³

Answer 1

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

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

where \( V \) is the volume and \( r \) is the radius of the sphere. Given that the radius \( r \) is 3.7 centimeters, we can substitute this value into the formula.

First, calculate \( r^3 \):

\[
r^3 = (3.7)^3 = 3.7 \times 3.7 \times 3.7 \approx 50.653
\]

Now, substitute \( r^3 \) into the volume formula:

\[
V = \frac{4}{3} \pi (50.653)
\]

Next, using \( \pi \approx 3.14159 \):

\[
V \approx \frac{4}{3} \times 3.14159 \times 50.653
\]

Calculating \( \frac{4}{3} \times \pi \):

\[
\frac{4}{3} \times 3.14159 \approx 4.18879
\]

Now multiply by \( 50.653 \):

\[
V \approx 4.18879 \times 50.653 \approx 212.17
\]

Therefore, the volume of the ball is approximately \( 212.17 \) cubic centimeters.

The closest measurement to the volume of the ball in cubic centimeters is:

**A: 212.17 cm³**