The ratio of radii of two spheres is 3: 5. Th | vedclass

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Question

(B) Let the radii of the two spheres be $r_1$ and $r_2$. Given that the ratio of their radii is $r_1 : r_2 = 3 : 5$.The surface area of a sphere is gi

Vedclass · Accepted Answer

$9: 25$

Vedclass · Answer

(B) Let the radii of the two spheres be $r_1$ and $r_2$. Given that the ratio of their radii is $r_1 : r_2 = 3 : 5$.The surface area of a sphere is given by the formula $S = 4\pi r^2$.The ratio of the surface areas of the two spheres is $\frac{S_1}{S_2} = \frac{4\pi r_1^2}{4\pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2$.Substituting the given ratio: $\frac{S_1}{S_2} = \left(\frac{3}{5}\right)^2 = \frac{9}{25}$.Thus,the ratio of their surface areas is $9: 25$.

The ratio of radii of two spheres is $3: 5$. Then,the ratio of their surface areas is $\ldots \ldots \ldots$.

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