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  • A solid cube is cut into 27 small cubes of equal volume. Find the ratio of the surface area of the given cube and that of the small cube.

A solid cube is cut into 27 small cubes of equal volume. Find the ratio of the surface area of the given cube and that of the small cube.

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Let the edge length of larger cube = A
and the edge length of smaller cube = a

Total volume will remain constant

Volume of larger cube = 27 × Volume of smaller cube

A³ = 27 × a³
Cube root on both sides
A = 3 a
A : a = 3 : 1

Ratio of surface area
= 6 × A² : 6 × a²
= A² : a²
= 9 : 1

∴ Ratio of their surface area is 9 : 1

 

Posted by

Deependra Verma

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