Answer:
The surface area of the sphere is 576π u²
Option D.
Step-by-step explanation:
First of all we need to calculate the radius
To calculate the radius of a sphere we have to use the following formula:
V = volume = 2304π u³
r = radius
π = pi
V = ⁴⁄₃πr³
we replace with the known values
2304π u³ = ⁴⁄₃ * π * (r)³
2304π u³ / (⁴⁄₃ * π) = (r)³
1728 u³ = (r)³
1728 u³ = (r)³
³
√(
1728 u³) = r
12 u = r
The radius of the sphere is 12 u
Now we can find the surface area
To calculate the area of a sphere we have to use the following formula:
A = area
r = radius = 12 u
π = pi
A = 4πr²
we replace with the known values
A = 4 * π * (12 u)²
A = 4 * π * 144 u²
A = 576π u²
The surface area of the sphere is 576π u²
