Question

If the surface areas of two spheres are in ratio 9:16 then find ratio of their radii

Answer 1

Let radius of first sphere be r and second sphere be R

Surface area of a sphere = 4$\pi r^{2}$

Ratio of surface areas = $\frac{4\pi r ^{2} }{4\pi R ^{2} }$

Ratio of surface areas = $\frac{r ^{2} }{R ^{2} }$

$\frac{r ^{2} }{R ^{2} }$ = $\frac{9}{16}$

$\frac{r}{R}$ = $\frac{3}{4}$

Hence the radii are in the ratio 3:4

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