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=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
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
Answers
GPT-4o mini
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**.
\[
V = \frac{4}{3} \pi r^3
\]
### 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**.