If the volumes of two cubes are in the ratio of 64 125 then whatis theratio of their total surface a...........

Quantitative Aptitude (MTS) Mensuration 3D

If the volumes of two cubes are in the ratio of 64 : 125, then whatis theratio of their total surface areas?

9 : 16

4 : 5

16 : 25

64 : 125

- The volume ratio of two cubes is given as 64:125.

- Let the side lengths of these cubes be \( a \) and \( b \).

- Since the volume of a cube is the cube of its side, \((a^3/b^3) = 64/125\).

- Taking the cube root on both sides gives \(a/b = \sqrt[3]{64}/\sqrt[3]{125} = 4/5\).

- The formula for the total surface area of a cube is 6 times the square of its side.

- So the surface area ratio is \((a^2/b^2) = (4/5)^2 = 16/25\).

- Option 3: 16:25

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