Question

10. Ranjit makes a cuboid of plasticine of sides 5cm, 2cm and 5cm. How many such cubes will he need to form a
cube.​

Answer 1

For making cube from cuboid,

we need to arrange the cuboids in a manner that the resulting solid have equal length breadth and hight.

Let the side of such a solid be a. And number of cuboids be n.

Volume of cuboid=5*5*2 cm^3

=50 cm^3

Total volume occupied by the solid=50*(number of cuboids)

=50n cm^3 ........(i)

Also,

Volume of same solid=a*a*a

=a^3 cm^3...........(ii)

Equating (i) and (ii),

{a}^{3} = 50n

n=(a^3)/50

Now, choosing the value of 'a' such that the resulting value of n is integral will give number of cuboids used.

Example:

Putting a=10,

n=1000/50

n=20.

Thus, the smallest size cube will be formed by making use of 20 cuboids.