Note: Figure is not drawn to scale
If the sphere shown above has a radius of 6 units, then what is the approximate volume of the sphere? (Use 3.14 for .)
A.
904.32 cubic units
B.
452.16 cubic units
C.
615.44 cubic units
D.
1,795.03 cubic units
Answers
Answered by
GPT-4o mini
To find the volume of a sphere, we 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 \( r \) is 6 units, we can substitute \( r \) and \( \pi \) (using 3.14 as the approximation):
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, calculate \( 6^3 \):
\[
6^3 = 216
\]
Now substitute that back into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculate \( \frac{4}{3} \times 216 \):
\[
\frac{4 \times 216}{3} = \frac{864}{3} = 288
\]
Now, multiply by \( 3.14 \):
\[
V = 288 \times 3.14 \approx 904.32
\]
Therefore, the approximate volume of the sphere is:
\[
\boxed{904.32} \text{ cubic units (Option A)}
\]
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Given that the radius \( r \) is 6 units, we can substitute \( r \) and \( \pi \) (using 3.14 as the approximation):
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, calculate \( 6^3 \):
\[
6^3 = 216
\]
Now substitute that back into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculate \( \frac{4}{3} \times 216 \):
\[
\frac{4 \times 216}{3} = \frac{864}{3} = 288
\]
Now, multiply by \( 3.14 \):
\[
V = 288 \times 3.14 \approx 904.32
\]
Therefore, the approximate volume of the sphere is:
\[
\boxed{904.32} \text{ cubic units (Option A)}
\]
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