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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