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18 July, 19:28

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

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  1. 18 July, 23:02
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    Given:

    A circle with an area of 225 π square feet.

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

    A = πr^2

    solve for r:

    225 π = 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 = 4500 π cubic feet

    The surface area of a sphere:

    SA = 4 πr^2

    SA = 4 π * (15^2)

    SA = 900 π square feet.

    Therefore the answer of this problem is letter A:

    A) A: V = 4500π ft3; S = 900π ft2
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