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Identify the volume and surface area of a sphere with great circle area 225π ft2 in terms of π.
A: V = 4500π ft3; S = 900π ft2
B: V = 900π ft3; S = 300π ft2
C: V = 900π ft3; S = 4500π ft2
D: V = 300π ft3; S = 900π ft2

Respuesta :

Hagrid
Given:

A circle with an area of 225π square feet.

We need to determine the volume and surface area of a sphere derived from this circle.

A = πr^2

solve for r:

225π = πr^2
225 = r^2
r = 15 feet

Volume of a sphere:

V = 4/3 π r^3
V = 4/3 π (15)^3
V = 4500π cubic feet

The surface area of a sphere:

SA = 4πr^2
SA = 4π * (15^2)
SA = 900π square feet. 

Therefore the answer of this problem is letter A:

A) A: V = 4500π ft3; S = 900π ft2

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