Question

A 5 × 5 × 5 cube is built using unit cubes. How many different cuboids (that differ in at least one unit

cube) can be formed using the same number of unit cubes?

Answer 1

Given :  5 × 5 × 5 cube is built using unit cubes.

To find :  How many different cuboids (that differ in at least one unit can be formed

Solution:

5 × 5 × 5 cube is built using unit cubes.

=> Volume = 125 cubic units

125 = 1 * 125  = 5  * 25  

1 , 5 , 25  & 125 are factor

Hence only possible Cuboids

125 =  1  * 1 * 125

125  = 1  * 5  * 25

only two Cuboids can be formed

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