Question
calculate the volume of a sphere using 3.14 for pi and round to the nearest tenth (the sphere has a diameter of 12)
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 \( r \) is the radius of the sphere. Since the diameter of the sphere is 12, the radius \( r \) is half of the diameter:
\[
r = \frac{12}{2} = 6
\]
Now we can substitute the radius and \( \pi \) (using 3.14) into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 6^3
\]
Calculating \( 6^3 \):
\[
6^3 = 216
\]
Now substituting this back into the volume equation:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculating \( \frac{4}{3} \times 216 \):
\[
\frac{4}{3} \times 216 = 288
\]
Now multiplying by \( 3.14 \):
\[
V = 288 \times 3.14 = 904.32
\]
Finally, rounding to the nearest tenth:
\[
V \approx 904.3
\]
Thus, the volume of the sphere is approximately **904.3 cubic units**.
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere. Since the diameter of the sphere is 12, the radius \( r \) is half of the diameter:
\[
r = \frac{12}{2} = 6
\]
Now we can substitute the radius and \( \pi \) (using 3.14) into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 6^3
\]
Calculating \( 6^3 \):
\[
6^3 = 216
\]
Now substituting this back into the volume equation:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculating \( \frac{4}{3} \times 216 \):
\[
\frac{4}{3} \times 216 = 288
\]
Now multiplying by \( 3.14 \):
\[
V = 288 \times 3.14 = 904.32
\]
Finally, rounding to the nearest tenth:
\[
V \approx 904.3
\]
Thus, the volume of the sphere is approximately **904.3 cubic units**.