Question

2. The ratio of the surface areas of two cubes is 49 : 81. Find the ratio of their volumes​

Answer 1

Answer: Ratio of their volumes => 343:729

Step-by-step explanation:

Let "a" be the side of 1st cube, and

"b" be the side of 2nd cube.  

Given, ratio of surface areas of two cubes are 49:81

Hence, 6a^2/6b^2 = 49/81        [Surface area of a cube=6(side)^2]

6 will cancel out, i.e., => a^2/b^2 = 49/81

=> (a/b)^2 =  49/81

=> a/b = 7/9      [49 is square of 7 and 81 is square of 9]

So, we got the side of 1st cube 'a' = 7 and,

side of 2nd cube 'b' = 9

Ratio of their volumes =>

a^3/b^3 = 7/9           [Volume of a cube = (side)^3]

(a/b)^3 = 7/9 => (7/9)^3 => 343/729

Ratio => 343:729

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Answer 2

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