Let's determine which of the given equations correctly calculates the volume of a sphere with a radius of 4 inches.
The volume [tex]\( V \)[/tex] of a sphere is calculated using the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
Given:
- The radius [tex]\( r = 4 \)[/tex] inches.
First, substitute the given radius into the volume formula:
[tex]\[
V = \frac{4}{3} \pi (4)^3
\][/tex]
Now let's check each of the given equations:
1. [tex]\( V = \frac{4}{3} \pi (4)^3 \)[/tex]
This matches the volume formula and correctly substitutes the radius [tex]\( r \)[/tex] with 4. Let's leave this equation for further evaluation.
2. [tex]\( V = \frac{4}{3} (4)^3 \)[/tex]
This equation is incorrect because it is missing the [tex]\( \pi \)[/tex] term. The volume of a sphere formula must include [tex]\( \pi \)[/tex].
3. [tex]\( V = \frac{2}{3} (8)^3 \)[/tex]
This equation is incorrect because the prefactor should be [tex]\( \frac{4}{3} \)[/tex]. Moreover, [tex]\( (8)^3 \)[/tex] does not reflect the cube of the radius provided, which should be 4.
4. [tex]\( V = \frac{2}{3} \pi (8)^3 \)[/tex]
This equation is incorrect for two reasons. Firstly, the prefactor should be [tex]\( \frac{4}{3} \)[/tex]. Secondly, [tex]\( (8)^3 \)[/tex] doesn't apply since the correct radius provided is 4.
After reviewing all options, the correct equation to find the volume of a sphere with a radius of 4 inches is:
[tex]\[
V = \frac{4}{3} \pi (4)^3
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{V = \frac{4}{3} \pi (4)^3}
\][/tex]
