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Find the surface area of the sphere if it has a volume of 2,304π cubic units.

A. 144 sq units
B. 288 sq units
C. 472 sq units
D. 576 sq units

Please help....

User Colapsnux
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1 Answer

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Answer:

The surface area of the sphere is 576π u²

Option D.

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

User Mikiqex
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