Let's find the volume of a sphere with a radius of 4 cm. We'll use the formula for the volume of a sphere, which is:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Here, [tex]\( r \)[/tex] is the radius of the sphere. Given that the radius [tex]\( r \)[/tex] is 4 cm, we can substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (4)^3 \][/tex]
First, calculate the cube of the radius:
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
Next, substitute this back into the formula:
[tex]\[ V = \frac{4}{3} \pi \times 64 \][/tex]
Multiplying out the constants and [tex]\(\pi\)[/tex]:
[tex]\[ V = \frac{256}{3} \pi \][/tex]
[tex]\[ V \approx 268.082573106329 \][/tex]
To find the volume to the nearest whole number, we round 268.082573106329:
[tex]\[ V \approx 268 \][/tex]
Thus, the volume of the sphere to the nearest whole number is:
[tex]\[ \boxed{268 \, \text{cm}^3} \][/tex]
Therefore, the correct answer is:
C. [tex]$268 \, cm^3$[/tex]
