What is the edge of the third smaller cube?

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube?

  1. 8 cm
  2. 10 cm
  3. 12 cm
  4. None of these
Anurag Mishra Professor Asked on 8th January 2016 in Maths.
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1 Answer(s)

Answer: (2) 10 cm 

Explanation:-
The age of a metal cube =12 cm
Therefore the volume of the cube = 12 x 12 x 12
= 1728 cm ^3

The age of first smaller cube = 6 cm
Therefore, the volume of the cube = 6 x  6 x 6
= 216 cm^3

The age of second smaller cube = 8 cm
Therefore, the volume of the cube = 8 x 8 x 8
= 512 cm cube

So, the volume of the third smaller cube = 1728 – (216 + 512)
= 1728 – 728
= 1000 cm^3

Thus, the age of the third smaller cube = cube root of (1000)
= 10 cm

Then, the age of the third smaller cube is 10 cm.

Hence, the correct answer is option (2) 10 cm.

Anurag Mishra Professor Answered on 8th January 2016.
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