2 cubes have volumes in the ratio 1:27. The r | vedclass

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(D) Let the side lengths of the two cubes be $a_1$ and $a_2$ respectively.The ratio of their volumes is given by $\frac{a_1^3}{a_2^3} = \frac{1}{27}$.

Vedclass · Accepted Answer

$1:9$

Vedclass · Answer

(D) Let the side lengths of the two cubes be $a_1$ and $a_2$ respectively.The ratio of their volumes is given by $\frac{a_1^3}{a_2^3} = \frac{1}{27}$.Taking the cube root on both sides,we get $\frac{a_1}{a_2} = \sqrt[3]{\frac{1}{27}} = \frac{1}{3}$.The area of a face of a cube is given by $a^2$.Therefore,the ratio of the area of the face of one cube to the other is $\frac{a_1^2}{a_2^2} = \left(\frac{a_1}{a_2}\right)^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9}$.Thus,the required ratio is $1:9$.

$2$ cubes have volumes in the ratio $1:27$. The ratio of the area of the face of one to that of the other is

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