The surface area of a sphere and the curved s | vedclass

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(B) Let the radius of the sphere be $r_1$ and the radius of the hemisphere be $r_2$.The surface area of a sphere is given by $4\pi r_1^2$.The curved s

Vedclass · Accepted Answer

$1: \sqrt{2}$

Vedclass · Answer

(B) Let the radius of the sphere be $r_1$ and the radius of the hemisphere be $r_2$.The surface area of a sphere is given by $4\pi r_1^2$.The curved surface area of a hemisphere is given by $2\pi r_2^2$.According to the problem,the surface areas are equal:$4\pi r_1^2 = 2\pi r_2^2$Dividing both sides by $2\pi$,we get:$2r_1^2 = r_2^2$Taking the square root on both sides:$\sqrt{2}r_1 = r_2$Therefore,the ratio of their radii is:$\frac{r_1}{r_2} = \frac{1}{\sqrt{2}}$Thus,the ratio is $1: \sqrt{2}$.

The surface area of a sphere and the curved surface area of a hemisphere are equal. Find the ratio of their radii.

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