Question

The sphere's radius is half the radius of the hemisphere. How does the volume of this hemisphere compare with the volume of the sphere?

Answer 1

Volume of Hemisphere = 4 times the volume of sphere.

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Answer 2

let the radius of hemisphere be r

given,

radius of sphere = radius of hemisphere /2

= r /2

so,

volume of sphere = (4/3)×π×(radius) ³

= (4/3)π (r/2)³

= (4/3)π(r³/8)

= πr³/6

and,

volume of hemisphere = (2/3)×π×(radius) ³

= (2/3) ×π ×r³

= 2πr³/3

hence, the volume of sphere is one-fourth of the volume of hemisphere..... (devide volume of hemisphere by volume of sphere)

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