The volume of two cubes are in the ratio 8:64, the ratio of their surface areas is(a) 1:4(6) 4:1(c) 1:1 (d) 4:3 . Created by tahirali76443. Math

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

taehyung21

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

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$

TaeTaePopsicle

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

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Answer :-1:4

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