Answer:
The correct volume is[tex]\( \frac{32}{3} \pi \)[/tex]cubic feet.
Step-by-step explanation:
To find the volume of a sphere given its surface area, you can use the formula:
[tex]\[ A = 4\pi r^2 \][/tex]
Where [tex]\( A \)[/tex] is the surface area and [tex]\( r \)[/tex] is the radius of the sphere.
Given that the surface area is \( 16\pi \) square feet, we can set up the equation:
[tex]\[ 16\pi = 4\pi r^2 \][/tex]
Dividing both sides by \( 4\pi \), we get:
[tex]\[ r^2 = 4 \][/tex]
Taking the square root of both sides, we find:
[tex]\[ r = 2 \][/tex]
Now, to find the volume of the sphere, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Substituting the value of [tex]\( r \),[/tex] we get:
[tex]\[ V = \frac{4}{3} \pi (2)^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi (8) \][/tex]
[tex]\[ V = \frac{32}{3} \pi \][/tex]
Therefore, the volume of the sphere is [tex]\( \frac{32}{3} \pi \)[/tex] cubic feet.
However, this volume doesn't match any of the given options. There might be a mistake in the options provided. The correct volume is[tex]\( \frac{32}{3} \pi \)[/tex]cubic feet.
