The ratio of radii of two spheres is 3:2. The | vedclass

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(D) Let the radii of the two spheres be $r_{1}$ and $r_{2}$ units.Given that the ratio of their radii is $\frac{r_{1}}{r_{2}} = \frac{3}{2}$.The surfa

Vedclass · Accepted Answer

$9:4$

Vedclass · Answer

(D) Let the radii of the two spheres be $r_{1}$ and $r_{2}$ units.Given that the ratio of their radii is $\frac{r_{1}}{r_{2}} = \frac{3}{2}$.The surface area of a sphere is given by the formula $A = 4\pi r^{2}$.The ratio of the surface areas of the two spheres is $\frac{A_{1}}{A_{2}} = \frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}$.Simplifying this,we get $\frac{A_{1}}{A_{2}} = \left(\frac{r_{1}}{r_{2}}\right)^{2}$.Substituting the given ratio: $\frac{A_{1}}{A_{2}} = \left(\frac{3}{2}\right)^{2} = \frac{9}{4}$.Therefore,the ratio of their surface areas is $9:4$.

The ratio of radii of two spheres is $3:2$. Then,the ratio of their surface areas is $\ldots \ldots \ldots \ldots$

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