The diameters of two spheres are in the ratio | vedclass

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(D) Let the diameters of the two spheres be $d_1$ and $d_2$. Given that $d_1 : d_2 = 3 : 5$.Since the radius $r = d/2$,the ratio of their radii $r_1 :

Vedclass · Accepted Answer

$27: 125$

Vedclass · Answer

(D) Let the diameters of the two spheres be $d_1$ and $d_2$. Given that $d_1 : d_2 = 3 : 5$.Since the radius $r = d/2$,the ratio of their radii $r_1 : r_2$ is also $3 : 5$.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.The ratio of the volumes of the two spheres is $\frac{V_1}{V_2} = \frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} = \left( \frac{r_1}{r_2} \right)^3$.Substituting the given ratio,we get $\left( \frac{3}{5} \right)^3 = \frac{27}{125}$.Therefore,the ratio of their volumes is $27 : 125$.

The diameters of two spheres are in the ratio $3: 5$. What is the ratio of their volumes?

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