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

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Question

(B) The volume $V$ of a sphere with radius $r$ is given by the formula $V = \frac{4}{3} \pi r^3$.Let the radii of the two spheres be $r_1$ and $r_2$.

Vedclass · Accepted Answer

$8:27$

Vedclass · Answer

(B) The volume $V$ of a sphere with radius $r$ is given by the formula $V = \frac{4}{3} \pi r^3$.Let the radii of the two spheres be $r_1$ and $r_2$. Given that $\frac{r_1}{r_2} = \frac{2}{3}$.The ratio of their volumes 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: $\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27}$.Thus,the ratio of their volumes is $8:27$.

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

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