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2 cubes have their volumes in the ratio 1:8 . the ratio of their surface area is-

a)1:2

b) 1:4

c) 1:9

d) 1:16

let side of smaller cobe be a1 and bigger cube be a2

ratio of their volume = 1/8 

(a1)3 / (a2)3 = 1/8 

a1/a2 = cube root(1/8)

a1/a2 = 1/2

therefore

a1 = 1 

and a2 = 2

ratio of their surface area= 4(a1)2/4(a2)2

= 4* (1)2/ 4 *(2)2

=4 / 16

= 1/4

therefore their ratio is 1:4 

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b)1: 4

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answer is b) 1:4

let side of 1 cube l and other be L

l3:L3 = 1:8 

l/L = 1/2

now for surface area:

6l2/ 6L2 = 6 l2/ 6 L2 = 1/4

hence answer is 1:4

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let the sides of cube be s & S

therefore

s3/S3= 1/8

or s/S= 1/ 2. . .... ... .   . .........(1)

multiplying the numerator by 6s and denominator by 6S of both sides

6s2 / 6S2= 6s/ 6Sx2

therefore surface area of smaller /surface area of bigger one = 6x1/ 6x2x2

therefore the required ratio is 1:4

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