Question

Parikshit makes a cuboid of plasticine of sides 5 cm 2 cm and 5 cm how many such cuboids will he need to form a cube

Answer 1

Well if dimensions of cube are 5*5*5 then he will need 2.5 such cuboids. For 10*10*10 cube he would need 20 of them.

Answer 2

( Refer to the first attachment )

Here, some cuboids of size 5 x 2 x 5 are given.

When these cuboids are arranged to form a cube, the side of this cube so formed will be a common multiple of the sides (i.e., 5, 2, and 5) of the given

cuboid.

LCM of 5, 2, and 5 = 10

Let us try to make a cube of 10 cm side.

For this arrangement, we have to put 2 cuboids along with its length, 5 along with its width, and 2 along with its height.

Total cuboids required according to this arrangement 2 x 5 x 2 = 20

With the help of 20 cuboids of such measures, a cube is formed as follows.

( Refer to the second attachment )

Alternatively

Volume of the cube of sides 5 cm, 2 cm, 5 cm

= 5 cm x 2 cm x 5 cm (5 x 5 x 2) cm3 Here, two 5s and one 2 are left which are not in a

triplet. If we multiply this expression by 2 x 2 x 5 = 20,

then it will become a perfect cube. Thus, (5x5x2x2x2 x 5) = (5 x 5 x 5 x 2 x 2 x 2) = 1000 is a perfect cube. Hence, 20 cuboids of 5 cm, 2 cm, 5 cm are required to form a cube.