# The Volumes of Two Cubes Are in the Ratio 1 : 27. the Ratio of Their Surface Area is - Mathematics

MCQ

The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is

• 1 : 3

• 1 : 8

• 1 : 9

•  1 : 18

#### Solution

1 : 9
Let the edges of the two cubes be a and b.
Then, ratio of their volumes     
Therefore,

"a"^1 /("b"^3) =1/27

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

=>"a"/"b"' = 1/3

The ratio of their surface areas =(6"a"^2)/(6"b"^2)

Therefore,

(6"a"^2)/(6b^2) = "a2"/"b2"

= 1/9 ["since " "a"/"b" = 1/5]

=1 : 9

Hence, the ratio of their surface areas is 1:9.

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Multiple Choice Questions | Q 47 | Page 922