Question

A sphere of maximum volume is cut out from a solid hemisphere of radius 7cm . Find the ratio of the volume of the hemisphere to that of the cut out sphere

Answer 1

here is your answer mate!

volume of sphere = 4/3πr^3

= 4/3×π×3.5×3.5×3.5

= 343/6×π

volume of hemisphere = 2/3πr^3

= 686/3×π

ratio = volume of hemisphere/ volume of sphere

= 686/3×π/ 343/6×π

= 4/1

therefore!, 4:1!

Answer 2

Ratio of the volume of the hemisphere to that of the cut out sphere  is 4 : 1

Solution:

Given that,

A sphere of maximum volume is cut out from a solid hemisphere of radius 7cm

The volume of hemisphere is given as:

$Volume\ of\ hemisphere = \frac{2}{3} \pi r^3 ------ eqn\ 1$

Where, r is the radius of hemisphere

The volume of sphere is given as:

A sphere of maximum volume is cut out from a solid hemisphere

$Volume\ of\ sphere = \frac{4}{3} \pi (\frac{r}{2})^3\\\\Volume\ of\ sphere = \frac{4 \pi r^3}{24} ----- eqn 2$

Find the ratio of the volume of the hemisphere to that of the cut out sphere

$\frac{\text{volume of hemisphere}}{\text{volume of cut out sphere}} = \frac{2}{3} \pi r^3 \div \frac{4 \pi r^3}{24}\\\\\frac{\text{volume of hemisphere}}{\text{volume of cut out sphere}} = \frac{2}{3} \pi r^3 \times \frac{24}{4 \pi r^3}\\\\\frac{\text{volume of hemisphere}}{\text{volume of cut out sphere}} = \frac{4}{1}$

Thus ratio of the volume of the hemisphere to that of the cut out sphere  is 4 : 1

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