Volumes of two spheres are in the ratio 64: 2 | vedclass

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(A) Let the radii of the two spheres be $r_1$ and $r_2$,respectively.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Given the ratio of v

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$16:9$

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(A) Let the radii of the two spheres be $r_1$ and $r_2$,respectively.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Given the ratio of volumes $V_1 : V_2 = 64 : 27$,we have:$\frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} = \frac{64}{27}$$\frac{r_1^3}{r_2^3} = \frac{64}{27} = \left(\frac{4}{3}\right)^3$Taking the cube root on both sides,we get:$\frac{r_1}{r_2} = \frac{4}{3}$The surface area of a sphere is given by $A = 4 \pi r^2$.The ratio of their surface areas is:$\frac{A_1}{A_2} = \frac{4 \pi r_1^2}{4 \pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2$Substituting the value of $\frac{r_1}{r_2}$:$\frac{A_1}{A_2} = \left(\frac{4}{3}\right)^2 = \frac{16}{9}$Thus,the ratio of their surface areas is $16:9$.

Volumes of two spheres are in the ratio $64: 27$. The ratio of their surface areas is

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