Maths / Cube and Cube Roots / Properties of Cubes of Numbers

QUESTION

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

 OPTIONS A. 1 : 3 B. 1 : 6 C. 1 : 9 D. 1 : 18
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

Let sides of two cubes be $a_1$ and $a_2$

So, $\frac{a^3_1}{a^3_2}=\frac{1}{27}$

Taking cube root, we get $\frac{a_1}{a_2}=\frac{1}{3}$

Area of face of first cube = $a^2_1$

And area of face of other cube = $a^2_2$

$\therefore$ Required ratio = $\frac{a^2_1}{a^2_2}=\left ( \frac{a_1}{a_2} \right )^2=\frac{1}{3}^2=\frac{1}{9}=1:9$

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