The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is

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KollegeApply · Accepted Answer

1 : 9 Let the edges of the two cubes be a and b. Then, ratio of their volumes ` Therefore, "a"^1 /("b"^3) =$\frac{1}{27}$ => (a/b)^3 = ($\frac{1}{3}$)^3 =>"a"/"b"' = $\frac{1}{3}$` The ratio of their surface areas =(6"a"^2)/(6"b"^2) Therefore, (6"a"^2)/(6b^2) = "a2"/"b2" `= $\frac{1}{9}$ ["since " "a"/"b" = $\frac{1}{5}$] =1 : 9` Hence, the ratio of their surface areas is 1:9.

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