Given a sphere with a radius of 4 cm, find its volume to the nearest whole number.

A. [tex]$85 \, cm^3$[/tex]
B. [tex]$67 \, cm^3$[/tex]
C. [tex][tex]$268 \, cm^3$[/tex][/tex]
D. [tex]$18 \, cm^3$[/tex]



Answer :

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]