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(C) The volume of the large cube is equal to the sum of the volumes of the three smaller cubes.Volume of large cube $= 3^3 + 4^3 + 5^3 = 27 + 64 + 125

Vedclass · Accepted Answer

$25:18$

Vedclass · Answer

(C) The volume of the large cube is equal to the sum of the volumes of the three smaller cubes.Volume of large cube $= 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216\, cm^3$.Side of the large cube $= \sqrt[3]{216} = 6\, cm$.Total surface area of the three smaller cubes $= 6(3^2) + 6(4^2) + 6(5^2) = 6(9 + 16 + 25) = 6(50) = 300\, cm^2$.Total surface area of the large cube $= 6(6^2) = 6(36) = 216\, cm^2$.The ratio of the total surface areas of the smaller cubes to the large cube is $\frac{300}{216}$.Dividing both by $12$,we get $\frac{25}{18}$ or $25:18$.

$A$ large cube is formed from the material obtained by melting three smaller cubes of sides $3\, cm$,$4\, cm$,and $5\, cm$ respectively. What is the ratio of the total surface areas of the smaller cubes to the large cube?

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