Question

two cubes have their volumes in the ratio 1:27 find the ratio of their surface areas

Answer 1

Let their edges be a and b. Then,

a^3/b^3 = 1/27

(or)

(a/b)^3 = (1/3)3

(or)


(a/b) = (1/3).

Ratio of their surface area

= 6a^2/6b^2

= a^2/b^2

= (a/b)^2

= 1/9

Answer 2

Let the radii of spheres be a and b

According to question,

V1 / V2 = 1 /27

=> (4 /3 pi a^3) / ( 4/3 pi b^3) = 1/ 27

=> a^3 / b^3 = 1/ 27

=> ( a / b)^3 = ( 1/ 3)^3

=> a / b = 1 /3 --------(1)

Now,

S1 / S2 = (4 pi a^2) / (4 pi b^2)

= (a / b)^2

= ( 1/ 3)^2

= 1 / 9

Required ratio = 1 : 9