Question

If the diameter of a youth softball is 3.5 in.
and the diameter of an adult softball is 3.8 in.
, what is the approximate difference in their volumes?

Use 3.14 for π
and round your answer to the nearest tenth.

V=43πr3
(1 point)
Responses

51.1 in3
51.1 in3

409.2 in3
409.2 in3

67.0 in3
67.0 in3

6.3 in3
6.3 in3

Answer 1

To find the difference in volumes between a youth softball and an adult softball, we first need to calculate their respective volumes using the formula for the volume of a sphere:

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

where \( r \) is the radius of the sphere.

1. **Calculate the radius of each softball:**
- For the youth softball with a diameter of 3.5 in:
\[
r_{\text{youth}} = \frac{3.5}{2} = 1.75 \text{ in}
\]
- For the adult softball with a diameter of 3.8 in:
\[
r_{\text{adult}} = \frac{3.8}{2} = 1.9 \text{ in}
\]

2. **Calculate the volume of the youth softball:**
\[
V_{\text{youth}} = \frac{4}{3} \times 3.14 \times (1.75)^3
\]
First, calculate \( (1.75)^3 \):
\[
(1.75)^3 = 5.359375
\]
Now we can calculate the volume:
\[
V_{\text{youth}} = \frac{4}{3} \times 3.14 \times 5.359375 \approx \frac{4}{3} \times 16.83546 \approx 22.4472 \text{ in}^3
\]

3. **Calculate the volume of the adult softball:**
\[
V_{\text{adult}} = \frac{4}{3} \times 3.14 \times (1.9)^3
\]
First, calculate \( (1.9)^3 \):
\[
(1.9)^3 = 6.859
\]
Now we can calculate the volume:
\[
V_{\text{adult}} = \frac{4}{3} \times 3.14 \times 6.859 \approx \frac{4}{3} \times 21.56346 \approx 28.7486 \text{ in}^3
\]

4. **Calculate the difference in volumes:**
\[
\text{Difference} = V_{\text{adult}} - V_{\text{youth}} \approx 28.7486 - 22.4472 = 6.3014 \text{ in}^3
\]

Rounding this to the nearest tenth, we get:

\[
\text{Approximate difference} \approx 6.3 \text{ in}^3
\]

Thus, the answer is **6.3 in³**.