Question

If the diameter of a men’s basketball is 10 inches and a women’s is 9 inches, what is the approximate difference of their volumes?
133.9 in.3
137.6 in.3
141.9 in.3
145.6 in.3

Answer 1

To find the difference in the volumes of a men's basketball and a women's basketball, we can use the formula for the volume of a sphere:

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

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

1. **Calculate the radius of each basketball**:
- Men's basketball: diameter = 10 inches, so radius \( r_m = \frac{10}{2} = 5 \) inches.
- Women's basketball: diameter = 9 inches, so radius \( r_w = \frac{9}{2} = 4.5 \) inches.

2. **Calculate the volume of the men's basketball**:
\[
V_m = \frac{4}{3} \pi (5)^3
\]
\[
= \frac{4}{3} \pi (125)
\]
\[
= \frac{500}{3} \pi \approx \frac{500 \times 3.14159}{3} \approx 523.6 \text{ in}^3
\]

3. **Calculate the volume of the women's basketball**:
\[
V_w = \frac{4}{3} \pi (4.5)^3
\]
\[
= \frac{4}{3} \pi (91.125)
\]
\[
= \frac{364.5}{3} \pi \approx 121.5 \pi \approx 381.0 \text{ in}^3
\]

4. **Calculate the difference in volumes**:
\[
\Delta V = V_m - V_w
\]
\[
\Delta V \approx 523.6 - 381.0 = 142.6 \text{ in}^3
\]

Thus, the approximate difference in volumes is about **141.9 in.³**, which is one of the choices given.

The answer is: **141.9 in.³**.