Question

The diameter of a men's basketball is 10 inches and a women's basketball is 9 inches. What is the approximate difference of their volumes?

Use 3.14 for π
.

V=43πr3
(1 point)
Responses

381.51 in3
381.51 in3

141.82 in3
141.82 in3

904.84 in3
904.84 in3

523.33 in3

Answer 1

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

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

First, we need to calculate the radius of both the men's and women's basketballs.

1. **Men's Basketball:**
- Diameter = 10 inches, so the radius \( r = \frac{10}{2} = 5 \) inches.
- Volume:
\[
V_m = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) = \frac{500}{3} \pi
\]
Substituting \( \pi \approx 3.14 \):
\[
V_m \approx \frac{500}{3} \times 3.14 \approx 523.33 \text{ in}^3
\]

2. **Women's Basketball:**
- Diameter = 9 inches, so the radius \( r = \frac{9}{2} = 4.5 \) inches.
- Volume:
\[
V_w = \frac{4}{3} \pi (4.5)^3 = \frac{4}{3} \pi (91.125) \approx \frac{364.5}{3} \pi
\]
Substituting \( \pi \approx 3.14 \):
\[
V_w \approx \frac{364.5}{3} \times 3.14 \approx 381.51 \text{ in}^3
\]

Now, we calculate the difference in volumes:

\[
\text{Difference} = V_m - V_w
\]
\[
\text{Difference} \approx 523.33 \text{ in}^3 - 381.51 \text{ in}^3 \approx 141.82 \text{ in}^3
\]

Thus, the approximate difference of their volumes is:

**141.82 in³**.