Question

Two cubes have volumes in the ratio 64:125 The ratio of the area of a face of first cube to

Answer 1

Given :-

Ratio between the volumes if the cubes is 64 : 125

Let their volumes be 64 cubic units and 125 cubic units respectively.

And the sides the cubes be x and y respectively.

We know that,

Side³ = volume of a cube

➡ x³ = 64 cubic units

➡ x = ³√64

➡ x = 4 units

Similarly,

➡ y³ = 125 cubic units

➡ y = ³√125

➡ y = 5 units

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]

= 6(4)²/6(5)²

= (6 × 16)/(6 × 25)

= 96/150

= 16/25

Hence, ratio of their total surface areas is 16 : 25

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