Question

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Answer 1

➡️Answer:

Ratio of their surface area is 1 : 9.

➡️Step-by-step explanation:

Volume of cubes = edge ^3

Let side of cube1 be a1

And side of cube2 be a2.

Then

(a1) ^3/ (a2) ^3 = 1 : 27

(given that ratio of vol is 1 : 27)

Taking cube root on each side :

a1 / a2 = 1 : 3

Ratio of sides = 1 : 3.

➡️ Surface area of cube = 6 side^2

➡️ Surface area of cube 1 = 6 ☓ (a1)^2

➡️ Surface area of cube 2 = 6 ☓ (a2)^2

Surface area of cube1 /surface area of cube 2

= 6 x a1^2/ 6 ☓ a2^2

= a1^2/a2^2

= (a1/a2) ^2. [using identity that :

a^m/b^m = (a/b) ^m]

= (1/3) ^2

= 1 /9

Hence,

We get

Ratio of surface area= 1 : 9