Question

The volume of two cubes are in the ratio 8:64, the ratio of their surface areas is<br />(a) 1:4<br />(6) 4:1<br />(c) 1:1 <br /> (d) 4:3 <br />​

Answer 1

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The volume of two cubes are in the ratio 8:64, the ratio of their surface areas is<br />(a) 1:4<br />(6) 4:1<br />(c) 1:1 <br /> (d) 4:3 <br />

Answer :-1:4

Let, Volume of the first cube \(= a_1^3\) Volume of the second cube \(= a_2^3\)

Now,

The volume of two cubes in ratio

$\(\Rightarrow \frac{{a_1^3}}{{a_2^3}} = \frac{8}{{64}}\) \(\Rightarrow \frac{{{a_1}}}{{{a_2}}} = \sqrt[3] {{\frac{8}{{64}}}} = \frac{2}{4} \frac{1}{2}\) Surface area of the first cube \(= 6a_1^2\) Surface area of the second cube \(= 6a_2^2\) Ratio of their surface area \(\Rightarrow \frac{{6a_1^2}}{{6a_1^2}} = \frac{{a_1^2}} {{a_2^2}}={\left({\frac{{{a_1}}}{{{a_2}}}} \right)^2}={\left({\frac{1}{2}} \right)^2} = \frac{1}{4}\, 1:4\)$

Answer 2

The volume of two cubes are in the ratio 8:64, the ratio of their surface areas is<br />(a) 1:4<br />(6) 4:1<br />(c) 1:1 <br /> (d) 4:3 <br />