Question

Calculate the volume of the sphere with a height of 12cm.. Use 3.14 for pi and round to the nearest tenth.

Answer 1

To find the volume of a sphere, we use the formula:

\[
V = \frac{4}{3} \pi r^3
\]

where \( r \) is the radius of the sphere.

From the problem, the height of the sphere is given as 12 cm. The height of a sphere is equal to its diameter, so we can find the radius:

\[
\text{Diameter} = 12 \, \text{cm} \implies r = \frac{\text{Diameter}}{2} = \frac{12}{2} = 6 \, \text{cm}
\]

Now we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]

First, we calculate \( (6)^3 \):

\[
(6)^3 = 6 \times 6 \times 6 = 216
\]

Now substitute that value into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 216
\]

Calculating \( \frac{4}{3} \times 216 \):

\[
\frac{4 \times 216}{3} = \frac{864}{3} = 288
\]

So now we can find the volume:

\[
V = 3.14 \times 288
\]

Calculating \( 3.14 \times 288 \):

\[
V = 903.92
\]

Now rounding to the nearest tenth, we find:

\[
V \approx 903.9 \, \text{cm}^3
\]

Thus, the volume of the sphere is approximately \( \boxed{903.9} \, \text{cm}^3 \).