Question

the ratio of surface area of two cubes is 16 : 49. find the ratio of their volume ​

Answer 1

Answer:

4:7 is the answer

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Answer 2

Step-by-step explanation:

Given:-

the ratio of surface area of two cubes is 16 : 49.

To find:-

find the ratio of their volumes.

Solution:-

Let the sides of the two cubes are a and b units

The Total surface area of a cube =6a² sq.units

The total surface area of the another cube=

6b² sq.units

Their ratio =6a²:6b²

=>a²:b²

According to the given problem,

the ratio of surface area of two cubes is 16 : 49

=>a²:b²=16:49

=>a²/b²=16/49

=>(a/b)²=16/49

=>a/b=√(16/49)

=>a/b=4/7

Let a=4x and b=7x

Volume of the first cube=a³ cubic units

=>a³=(4x)³=64x³ cubic units

Volume of the second cube=b³ cubic units

=>b³=(7x)³=343 x³ cubic units

Ratio of Volumes of the two cubes

=>a³:b³

=>64x³:343x³

=>64x³/343x³

=>64/343

=>64:343

Answer:-

The ratio of their volumes =64:343