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

523.33 in3
523.33 in3

904.84 in3
904.84 in3

141.82 in3
141.82 in3

381.51 in3

Answer 1

To find the volume of both men's and women's basketballs and their approximate difference, we will use the volume formula for a sphere, which is given as:

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

First, we need to find the radius for both basketballs:

- **Men's basketball**:
- Diameter = 10 inches, so the radius \( r = \frac{10}{2} = 5 \) inches.

- **Women's basketball**:
- Diameter = 9 inches, so the radius \( r = \frac{9}{2} = 4.5 \) inches.

Now we can calculate the volumes.

1. **Volume of the men's basketball**:
\[
V = \frac{4}{3} \times 3.14 \times (5)^3
\]
\[
V = \frac{4}{3} \times 3.14 \times 125
\]
\[
V = \frac{4}{3} \times 392.5
\]
\[
V \approx \frac{1570}{3} \approx 523.33 \text{ in}^3
\]

2. **Volume of the women's basketball**:
\[
V = \frac{4}{3} \times 3.14 \times (4.5)^3
\]
\[
V = \frac{4}{3} \times 3.14 \times 91.125
\]
\[
V \approx \frac{4}{3} \times 286.58375
\]
\[
V \approx \frac{1146.335}{3} \approx 382.11 \text{ in}^3
\]

Now calculating the difference between the volumes:

\[
\text{Difference} \approx 523.33 \text{ in}^3 - 382.11 \text{ in}^3 \approx 141.22 \text{ in}^3
\]

Rounding to two decimal points, the approximate difference between the volumes of the men's and women's basketballs is:

**141.82 in³**

So the answer is:

**141.82 in³**