Question

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube ?

Answer 1

Sides of a cuboid are 5cm,2cm and 5cm 
Volume of cuboid =5×2×5=50 cm³ 

Let the side of the cube formed with minimum number of cuboids =x 

Hence volume of the cube =x³ 

Number of cuboids required = n 

Hence n×50 =x³ 

n×50 must be perfect cube 

n×2×5×5 

i.e minmum value of n= 2×2×5=20 

Volume of the cube formed =20×50=1000 cm³ 

and Side of the cube = 10 cm

Answer 2

cuboid :  5 X 5 X 2 cm
to make it a cube, all sides are to be equal.  We can put 5 cuboids along the dimension of 2 cm to make it 10 cm side...

so we get a cube of : 10 X 10 X 10 cm
number of cuboids needed:  2 * 2 * 5 = 20