question_answer

Two cubes have volumes is the ratio 1: 64. The ratio of the area of a face of first cube to the of other is?

Answer:

Volume,

\[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{1}{64}\]

\[\frac{a_{1}^{3}}{a_{2}^{3}}=\frac{1}{64}\]

\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{4}\]

Area of first face for first cube \[={{a}_{1}}\times {{a}_{1}}\]

\[=1\times 1\]

Area of first face of other cube \[={{a}_{2}}\times {{a}_{2}}\]

= 4 × 4

Ratio will be \[=\frac{1}{16}\]