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=4 over 3πr3


(1 point)
Responses

381.51 in3
381.51 in3

904.84 in3
904.84 in3

141.82 in3
141.82 in3

523.33 in3
523.33 in3

1 answer

To find the difference in volumes between a men's basketball and a women's basketball, we first need to calculate the volumes of both basketballs using the formula for the volume of a sphere:

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

Step 1: Calculate the volume of the men's basketball:

  1. The diameter of the men's basketball is 10 inches, so the radius \( r \) is half of the diameter:

    \[ r = \frac{10}{2} = 5 \text{ inches} \]

  2. Now we can substitute the radius into the volume formula:

    \[ V = \frac{4}{3} \times 3.14 \times (5)^3 \]

  3. Calculate \( (5)^3 \):

    \[ (5)^3 = 125 \]

  4. Now substitute it back into the volume formula:

    \[ V = \frac{4}{3} \times 3.14 \times 125 \]

  5. Calculate \( \frac{4}{3} \times 3.14 \):

    \[ \frac{4}{3} \times 3.14 \approx 4.1867 \]

  6. Now multiply by 125:

    \[ V \approx 4.1867 \times 125 \approx 523.33 \text{ in}^3 \]

Step 2: Calculate the volume of the women's basketball:

  1. The diameter of the women's basketball is 9 inches, so the radius \( r \) is:

    \[ r = \frac{9}{2} = 4.5 \text{ inches} \]

  2. Substitute the radius into the volume formula:

    \[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \]

  3. Calculate \( (4.5)^3 \):

    \[ (4.5)^3 = 91.125 \]

  4. Now substitute it back into the volume formula:

    \[ V = \frac{4}{3} \times 3.14 \times 91.125 \]

  5. Calculate \( \frac{4}{3} \times 3.14 \):

    \[ \frac{4}{3} \times 3.14 \approx 4.1867 \]

  6. Now multiply by 91.125:

    \[ V \approx 4.1867 \times 91.125 \approx 381.51 \text{ in}^3 \]

Step 3: Find the difference in volumes:

Now we can find the difference between the volumes of the men's and women's basketballs:

\[ \text{Difference} = V_{\text{men}} - V_{\text{women}} \approx 523.33 - 381.51 \approx 141.82 \text{ in}^3 \]

Answer:

The approximate difference in their volumes is 141.82 in³.