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

523.33 in3
523.33 in3

141.82 in3
141.82 in3

904.84 in3

Answer 1

To calculate the volume of the men's and women's basketballs, we first need to find their respective radii from their diameters.

### Step 1: Find the Radii
- Men's basketball:
- Diameter = 10 inches, so the radius \( r_m = \frac{10}{2} = 5 \) inches.

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

### Step 2: Use the Volume Formula
The formula for the volume of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
\]

Using \( \pi \approx 3.14 \):

#### Volume of the Men's Basketball:
\[
V_m = \frac{4}{3} \times 3.14 \times (5)^3
\]
\[
V_m = \frac{4}{3} \times 3.14 \times 125
\]
\[
V_m = \frac{4 \times 3.14 \times 125}{3}
\]
\[
V_m = \frac{1570}{3} \approx 523.33 \, \text{in}^3
\]

#### Volume of the Women's Basketball:
\[
V_w = \frac{4}{3} \times 3.14 \times (4.5)^3
\]
\[
V_w = \frac{4}{3} \times 3.14 \times 91.125
\]
\[
V_w = \frac{4 \times 3.14 \times 91.125}{3}
\]
\[
V_w = \frac{1146.135}{3} \approx 382.05 \, \text{in}^3
\]

### Step 3: Calculate the Difference in Volumes
Now, we find the difference in volumes:
\[
\text{Difference} = V_m - V_w \approx 523.33 - 382.05
\]
\[
\text{Difference} \approx 141.28 \, \text{in}^3
\]

None of the provided responses match this number, so the closest response based on the options provided would be:

**141.82 in³**

Therefore, the approximate difference of their volumes is **141.82 in³**.