Two cubes have volumes in the ratio $1 : 64$ . The ratio of their sides is ____.

1 : 3

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1 : 4

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1 : 8

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8 : 1

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Solution

The correct option is B $1 : 4$
Given:
Volume ratio of two cubes is $1 : 64.$

Let side length of cube 1 be $a_{1} .$
Let side length of cube 2 be $a_{2} .$

Volume of cube 1 will be:
$V_{1} = a_{1}^{3}$
Volume of cube 2 will be:
$V_{2} = a_{2}^{3}$

Ratio of volumes is:
$\frac{V_{1}}{V_{2}} = \frac{a_{1}^{3}}{a_{2}^{3}}$
$\frac{1}{64} = {(\frac{a_{1}}{a_{2}})}^{3}$
$\frac{a_{1}}{a_{2}} = \frac{1}{4}$

Therefore, ratio of their sides is 1 : 4.

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Question 25

Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is
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Two cubes have volumes in the ratio 1:64. The ratio of their sides is ____.

The correct option is B 1:4Given: Volume ratio of two cubes is 1:64. Let side length of cube 1 be a1. Let side length of cube 2 be a2. Volume of cube 1 will be: V1=a31 Volume of cube 2 will be: V2=a32 Ratio of volumes is: V1V2=a31a32 164=(a1a2)3 a1a2=14 Therefore, ratio of their sides is 1 : 4.

Two cubes have volumes in the ratio $1 : 64$ . The ratio of their sides is ____.