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

904.84 in3
904.84 in3

381.51 in3
381.51 in3

141.82 in3
141.82 in3

523.33 in3

Answer 1

To find the difference in volume between 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. First, we need to determine the radius for each basketball:

- **Men's Basketball:**
- Diameter = 10 inches
- Radius = \( \frac{10}{2} = 5 \) inches

- **Women's Basketball:**
- Diameter = 9 inches
- Radius = \( \frac{9}{2} = 4.5 \) inches

Next, we will calculate the volumes of both basketballs using \( \pi \approx 3.14 \).

1. **Volume of the Men's Basketball:**
\[
V_{\text{men}} = \frac{4}{3} \times 3.14 \times (5)^3
\]
\[
= \frac{4}{3} \times 3.14 \times 125
\]
\[
= \frac{4 \times 3.14 \times 125}{3}
\]
\[
= \frac{1570}{3} \approx 523.33 \text{ in}^3
\]

2. **Volume of the Women's Basketball:**
\[
V_{\text{women}} = \frac{4}{3} \times 3.14 \times (4.5)^3
\]
\[
= \frac{4}{3} \times 3.14 \times 91.125
\]
\[
= \frac{4 \times 3.14 \times 91.125}{3}
\]
\[
= \frac{1130.208}{3} \approx 376.736 \text{ in}^3
\]

3. **Difference in Volume:**
\[
\text{Difference} = V_{\text{men}} - V_{\text{women}}
\]
\[
\approx 523.33 - 376.736 \approx 146.594 \text{ in}^3
\]

From the calculations, the estimated approximate difference in volumes is about \( 146.59 \text{ in}^3 \), which does not match exactly with the provided options.

However, the closest option to our calculated difference would be **141.82 in³**.

Thus, the correct response based on the given options would be:
**141.82 in³**.