The ratio of the radii of a sphere and a hemi | vedclass

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(C) Let the radius of the sphere be $r_1$ and the radius of the hemisphere be $r_2$.Given that the ratio of their radii is $r_1 : r_2 = 3 : 2$,so $\fr

Vedclass · Accepted Answer

$3:1$

Vedclass · Answer

(C) Let the radius of the sphere be $r_1$ and the radius of the hemisphere be $r_2$.Given that the ratio of their radii is $r_1 : r_2 = 3 : 2$,so $\frac{r_1}{r_2} = \frac{3}{2}$.The surface area of a sphere is $4 \pi r_1^2$.The total surface area of a hemisphere is $3 \pi r_2^2$.Now,the ratio of the surface area of the sphere to the total surface area of the hemisphere is:$\frac{4 \pi r_1^2}{3 \pi r_2^2} = \frac{4}{3} 	imes \left(\frac{r_1}{r_2}ight)^2$$= \frac{4}{3} 	imes \left(\frac{3}{2}ight)^2$$= \frac{4}{3} 	imes \frac{9}{4}$$= \frac{3}{1}$Therefore,the required ratio is $3:1$.

The ratio of the radii of a sphere and a hemisphere is $3:2$. Find the ratio of the surface area of the sphere to the total surface area of the hemisphere.

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