Question
A sphere has a radius r = 12 inches. What is its approximate volume to the nearest tenth? Use 3.14 for π.
A.
602.9 in3
B.
904.3 in3
C.
1,808.6 in3
D.
7,234.6 in3
A.
602.9 in3
B.
904.3 in3
C.
1,808.6 in3
D.
7,234.6 in3
Answers
GPT-4o mini
To calculate the volume of a sphere, you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Given that the radius \( r = 12 \) inches and using \( \pi \approx 3.14 \), the calculation proceeds as follows:
1. First, calculate \( r^3 \):
\[
r^3 = 12^3 = 12 \times 12 \times 12 = 1728
\]
2. Next, multiply by \( \pi \):
\[
\pi r^3 = 3.14 \times 1728
\]
Now calculating \( 3.14 \times 1728 \):
\[
3.14 \times 1728 \approx 5425.12
\]
3. Finally, multiply by \(\frac{4}{3}\):
\[
V = \frac{4}{3} \times 5425.12 \approx 7233.49
\]
Since we're looking for the volume to the nearest tenth, we can round this to:
\[
V \approx 7234.6 \, \text{in}^3
\]
Therefore, the closest answer from the given options is:
**D. 7,234.6 in³**
\[ V = \frac{4}{3} \pi r^3 \]
Given that the radius \( r = 12 \) inches and using \( \pi \approx 3.14 \), the calculation proceeds as follows:
1. First, calculate \( r^3 \):
\[
r^3 = 12^3 = 12 \times 12 \times 12 = 1728
\]
2. Next, multiply by \( \pi \):
\[
\pi r^3 = 3.14 \times 1728
\]
Now calculating \( 3.14 \times 1728 \):
\[
3.14 \times 1728 \approx 5425.12
\]
3. Finally, multiply by \(\frac{4}{3}\):
\[
V = \frac{4}{3} \times 5425.12 \approx 7233.49
\]
Since we're looking for the volume to the nearest tenth, we can round this to:
\[
V \approx 7234.6 \, \text{in}^3
\]
Therefore, the closest answer from the given options is:
**D. 7,234.6 in³**