The volume of two hemispheres is in the ratio | vedclass

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(A) Let the volumes of the two hemispheres be $V_1$ and $V_2$,and their radii be $r_1$ and $r_2$ respectively.The formula for the volume of a hemisphe

Vedclass · Accepted Answer

$2:3$

Vedclass · Answer

(A) Let the volumes of the two hemispheres be $V_1$ and $V_2$,and their radii be $r_1$ and $r_2$ respectively.The formula for the volume of a hemisphere is $V = \frac{2}{3} \pi r^3$.Given the ratio of volumes: $V_1 : V_2 = 8 : 27$.Substituting the formula: $\frac{\frac{2}{3} \pi r_1^3}{\frac{2}{3} \pi r_2^3} = \frac{8}{27}$.Simplifying the expression: $\frac{r_1^3}{r_2^3} = \frac{8}{27}$.Taking the cube root on both sides: $\frac{r_1}{r_2} = \sqrt[3]{\frac{8}{27}} = \frac{2}{3}$.Therefore,the ratio of their radii is $2:3$.

The volume of two hemispheres is in the ratio $8:27$. What is the ratio of their radii?

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