Question

Two cubes have their volumes in the ratio 1:8,then the ratio of their surface area is

Answer 1

Volume=1:8
Then side=1:2(since side^3 is volume in a cube)
Then surface Area=6:24=1:4(since 6*(side)^2 is the surface area in a cube)

ANS}1:4

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Answer 2

Answer:

If two cubes have their volumes in the ratio 1:8,then the ratio of their surface area is 1 : 4

Step-by-step explanation:

• Let the Volume of first cube be V1 =$a1^{3}$.

     And  Volume of second cube be V2 =$a2^{3}$.

     a1 and a2 are sides of respective cubes.

• Now, V1 : V2 = 1 : 8

      so, $a1^{3}$ : $a2^{3}$ = 1 : 8

       ⇒ a1 : a2 = 1 : 2

     Hence, a1/a2 = 1/2

     ⇒ a2 = 2.a1

• Surface area of any cube = 6$a^{2}$ , where a is the side of the cube.

• Surface area of 1 st cube is 6$a1^{2}$

• Surface area of 2 nd cube is =6$a2^{2}$  = 6 × a2 × a2 = 6×(2. a1) × (2 . a1)

     = 24 $a1^{2}$

• Ratio of surface area of 1st and 2nd cubes is 6$a1^{2}$ : 24$a1^{2}$ = 6 : 24

       = 1 : 4