Question
Calculate the volume of a sphere that has a radius of 8 cm using 3.14 for pi and round to the nearest tenth.(1 point)Responses2,143.6 cm32,143.6 cm cubed67.0 cm367.0 cm cubed100.5 cm3100.5 cm cubed267.9 cm3
Answers
Answered by
GPT-4o mini
To calculate the volume of a sphere, you can use the formula:
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius of the sphere. Given that the radius \( r = 8 \) cm and using \( \pi \approx 3.14 \), we can compute the volume as follows:
1. Calculate \( r^3 \):
\[
r^3 = 8^3 = 512
\]
2. Substitute into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 512
\]
3. First, calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]
4. Now, multiply by \( 512 \):
\[
V \approx 4.18667 \times 512 \approx 2145.34
\]
5. Rounding to the nearest tenth gives:
\[
V \approx 2145.3
\]
Hence, the volume of the sphere, rounded to the nearest tenth, is approximately 2145.3 cm³.
Since the calculated options provided do not match 2145.3 cm³ but round closely to 2143.6 cm³, I would adjust to select the closest available option:
**2143.6 cm³**
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius of the sphere. Given that the radius \( r = 8 \) cm and using \( \pi \approx 3.14 \), we can compute the volume as follows:
1. Calculate \( r^3 \):
\[
r^3 = 8^3 = 512
\]
2. Substitute into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 512
\]
3. First, calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]
4. Now, multiply by \( 512 \):
\[
V \approx 4.18667 \times 512 \approx 2145.34
\]
5. Rounding to the nearest tenth gives:
\[
V \approx 2145.3
\]
Hence, the volume of the sphere, rounded to the nearest tenth, is approximately 2145.3 cm³.
Since the calculated options provided do not match 2145.3 cm³ but round closely to 2143.6 cm³, I would adjust to select the closest available option:
**2143.6 cm³**