Question

a sphere of maximum value is cut out from a solid hemisphere of radius r. What is the ratio of the volume of the hemisphere to that of the cutout sphere?

Answer 1

A sphere ⚾ with maximum volume can be cut from a solid hemisphere will be one whose

Diameter is equal to the the Radius of the hemisphere

let r be the radius of hemisphere

Then radius of sphere = r / 2

volume of hemisphere. = 2 / 3π r^3

volume of sphere = 4 / 3π (r/2) ^ 3

RATIO = VOL.OF HEMI,SPH / VOL,OF, SPH

= 2/3πr^3. / 4/3π((r/2))^3
= 4

Therefore. ratio = 4 : 1

Answer 2

Answer:

A sphere ⚾ with maximum volume can be cut from a solid hemisphere will be one whose

Diameter is equal to the the Radius of the hemisphere

let r be the radius of hemisphere

Then radius of sphere = r / 2

volume of hemisphere. = 2 / 3π r^3

volume of sphere = 4 / 3π (r/2) ^ 3

RATIO = VOL.OF HEMI,SPH / VOL,OF, SPH

= 2/3πr^3. / 4/3π((r/2))^3

= 4

Therefore. ratio = 4 : 1