Question

Given a sphere with a diameter of 8 cm, find its volume to the nearest whole number.

A.
2144 cm3
B.
85 cm3
C.
268 cm3
D.
201 cm3

Answer 1

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 the diameter of the sphere is 8 cm, we can calculate the radius as follows:

\[
r = \frac{\text{diameter}}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]

Now we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (4 \, \text{cm})^3
\]

Calculating \( (4 \, \text{cm})^3 \):

\[
(4 \, \text{cm})^3 = 64 \, \text{cm}^3
\]

Now substituting this back into the volume formula:

\[
V = \frac{4}{3} \pi (64 \, \text{cm}^3) = \frac{256}{3} \pi \, \text{cm}^3
\]

Next, we need to compute \( \frac{256}{3} \) and then multiply it by \( \pi \) (approximately 3.14):

\[
V \approx \frac{256}{3} \times 3.14 \approx 85.333 \times 3.14
\]

Calculating \( \frac{256 \times 3.14}{3} \):

\[
256 \div 3 \approx 85.3333
\]
\[
85.3333 \times 3.14 \approx 267.999
\]

Rounding this to the nearest whole number gives us:

\[
268 \, \text{cm}^3
\]

Therefore, the volume of the sphere to the nearest whole number is:

\[
\boxed{268} \, \text{cm}^3
\]

So the correct answer is C. 268 cm³.