Question

the25 Two ubes have their volumes in ratio 1:64. What will be the ratio of their surface area?​

Answer 1

Answer :

1:16

Note :

• A cube has 6 faces , 8 vertices , 12 edges .

• Let the side of a cube be a , then ;

→ Volume = a³

→ Total surface area = 6a²

→ Lateral surface area = 4a²

Solution :

• Let a and a' be the sides of 1st and 2nd cube respectively .

• Let v and v' be the volumes of 1st and 2nd cube respectively .

• Let s and s' be the surface areas of 1st and 2nd cube respectively .

Here ,

It is given that , the ratio of volumes of 1st and 2nd cube is 1:64 .

Thus ,

=> v:v' = 1:64

=> v/v' = 1/64

=> a³/a'³ = 1/64

=> (a/a')³ = (1/4)³

=> a/a' = 1/4

Now ,

The ratio of surface areas of 1st and 2nd will be ;

=> s:s' = 6a²:6a'²

=> s/s' = a²/a'²

=> s/s' = (a/a')²

=> s/s' = (1/4)²

=> s/s' = 1/16

=> s:s' = 1:16

Hence ,

Required Ratio is 1:16 .