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# The Volumes of Two Cubes Are in the Ratio 8 : 27. Find the Ratio of Their Surface Areas. - Mathematics

Sum

The volumes of two cubes are in the ratio 8 : 27. Find the ratio of their surface areas.

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#### Solution

Let the edges of cubes be a and b.

As,

"Volume of the first cube"/"Volume of the second cybe" = 8/27

=> a^3/b^3 = 8/27

=> a/b = root(3)(8/27)

=>a/b = 2/3          .................(i)

Now,

The ratio of the surface areas of the cubes = "Surface area of the first cube"/"Surface area of the second cube"

= "6a"^2/"6b"^2

=("a"/"b")^2

=(2/3)^2          [Using (i)]

=4/9

So, the ratio of the surface areas of the given cubes is 4 : 9.

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise | Q 6 | Page 914
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