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Hint: Try to find out the volume of both hemispheres and cones and equate them.

Given,

Radius of Hemisphere $R = 7cm$

Height of cone $h = 49cm$

Volume of hemisphere $V = \dfrac{2}{3}\pi {R^3}$

$

= \dfrac{2}{3}\pi \times {\left( 7 \right)^3}{\text{ c}}{{\text{m}}^3} \\

= \dfrac{2}{3} \times 343 \times \pi {\text{ c}}{{\text{m}}^3} \\

= \dfrac{{686}}{3}\pi {\text{ c}}{{\text{m}}^3} \\

$

Volume of cone $V = \dfrac{1}{3}\pi {r^2}h$

$ = \dfrac{1}{3}\pi {r^2} \times 49{\text{ cm}}$

The hemisphere is cast into a right circular cone. So the volume of the hemisphere will be equal to the volume of the cone.

$\therefore $Volume of hemisphere = Volume of cone

$

\dfrac{{686}}{3}\pi c{m^3} = \dfrac{{49}}{3}\pi {r^2}cm \\

{r^2} = \dfrac{{686}}{3}{\text{ }}c{m^2} \\

{r^2} = 14{\text{ }}c{m^2} \\

r = \sqrt {14{\text{ }}c{m^2}} \\

r = \sqrt {14} {\text{ }}cm \\

r = 3.74{\text{ }}cm \\

$

Hence, radius of base of cone $r = 3.74{\text{ }}cm$

Note: Whenever there is one shape converted into another, always keep in mind that their volumes will always be the same. Alsoâ€™ the formula for volume of different shapes are already defined. Soâ€™ you only need to equate them.

Given,

Radius of Hemisphere $R = 7cm$

Height of cone $h = 49cm$

Volume of hemisphere $V = \dfrac{2}{3}\pi {R^3}$

$

= \dfrac{2}{3}\pi \times {\left( 7 \right)^3}{\text{ c}}{{\text{m}}^3} \\

= \dfrac{2}{3} \times 343 \times \pi {\text{ c}}{{\text{m}}^3} \\

= \dfrac{{686}}{3}\pi {\text{ c}}{{\text{m}}^3} \\

$

Volume of cone $V = \dfrac{1}{3}\pi {r^2}h$

$ = \dfrac{1}{3}\pi {r^2} \times 49{\text{ cm}}$

The hemisphere is cast into a right circular cone. So the volume of the hemisphere will be equal to the volume of the cone.

$\therefore $Volume of hemisphere = Volume of cone

$

\dfrac{{686}}{3}\pi c{m^3} = \dfrac{{49}}{3}\pi {r^2}cm \\

{r^2} = \dfrac{{686}}{3}{\text{ }}c{m^2} \\

{r^2} = 14{\text{ }}c{m^2} \\

r = \sqrt {14{\text{ }}c{m^2}} \\

r = \sqrt {14} {\text{ }}cm \\

r = 3.74{\text{ }}cm \\

$

Hence, radius of base of cone $r = 3.74{\text{ }}cm$

Note: Whenever there is one shape converted into another, always keep in mind that their volumes will always be the same. Alsoâ€™ the formula for volume of different shapes are already defined. Soâ€™ you only need to equate them.

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