The volumes of two cubes are in the ratio of | vedclass

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(A) Let the sides of the two cubes be $a_1$ and $a_2$.The ratio of their volumes is given by $\frac{V_1}{V_2} = \frac{a_1^3}{a_2^3} = \frac{8}{125}$.T

Vedclass · Accepted Answer

$2:5$ and $4:25$

Vedclass · Answer

(A) Let the sides of the two cubes be $a_1$ and $a_2$.The ratio of their volumes is given by $\frac{V_1}{V_2} = \frac{a_1^3}{a_2^3} = \frac{8}{125}$.Taking the cube root on both sides,the ratio of their edges is $\frac{a_1}{a_2} = \sqrt[3]{\frac{8}{125}} = \frac{2}{5}$.Thus,the ratio of their edges is $2:5$.The ratio of their surface areas is given by $\frac{6a_1^2}{6a_2^2} = \left(\frac{a_1}{a_2}\right)^2$.Substituting the edge ratio,we get $\left(\frac{2}{5}\right)^2 = \frac{4}{25}$.Therefore,the ratio of their surface areas is $4:25$.

The volumes of two cubes are in the ratio of $8: 125$. Find the ratio of their edges and surface areas.

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