Find the radius of a sphere whose surface,area and volume are equal
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The volume of a sphere is equal to the surface area of the sphere. If this value is equal to Nπ, what is the value of N?
The formula for the volume of a sphere is V=43πr3, where V is volume and r is radius length.
The formula for the surface area of a sphere is SA=4πr2, where SA is surface area and r is radius length.
Equate the two formulas together:
43πr3=4πr2
Then divide both sides of the equation by 4πr2 to obtain
13r=1, since r>0
Multiply both sides by 3 to get r=3.
The surface area is 4π(3)2=36π
Equating this result to what you are asking, N=36.
The formula for the volume of a sphere is V=43πr3, where V is volume and r is radius length.
The formula for the surface area of a sphere is SA=4πr2, where SA is surface area and r is radius length.
Equate the two formulas together:
43πr3=4πr2
Then divide both sides of the equation by 4πr2 to obtain
13r=1, since r>0
Multiply both sides by 3 to get r=3.
The surface area is 4π(3)2=36π
Equating this result to what you are asking, N=36.
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