To determine which sphere has a radius of 4 inches, we'll use the formula for the volume of a sphere.
The volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere. Given that the radius [tex]\( r \)[/tex] is 4 inches, we substitute [tex]\( r = 4 \)[/tex] into the formula:
[tex]\[ V = \frac{4}{3} \pi (4)^3 \][/tex]
Calculate [tex]\( 4^3 \)[/tex] (which is 4 cubed):
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
Now, substitute [tex]\( 64 \)[/tex] back into the volume equation:
[tex]\[ V = \frac{4}{3} \pi \times 64 \][/tex]
Simplify the multiplication:
[tex]\[ V = \frac{4 \times 64}{3} \pi \][/tex]
[tex]\[ V = \frac{256}{3} \pi \][/tex]
Therefore, the volume of the sphere with a radius of 4 inches is:
[tex]\[ \boxed{\frac{256}{3} \pi} \][/tex]
Given the choices:
1. [tex]\( V = \frac{32}{3} \pi \)[/tex] in[tex]\(^3\)[/tex]
2. [tex]\( V = 36 \pi \)[/tex] in[tex]\(^3\)[/tex]
3. [tex]\( V = \frac{256}{3} \pi \)[/tex] in[tex]\(^3\)[/tex]
4. [tex]\( V = 288 \pi \)[/tex] in[tex]\(^3\)[/tex]
The sphere with the calculated volume [tex]\(\frac{256}{3} \pi\)[/tex] cubic inches matches option 3.
Thus, the sphere with a radius of 4 inches is described by option:
[tex]\[ \boxed{3} \][/tex]
