Question

b) Rohit makes a cuboid of dimensions 5 cm, 2cm, and 5 cm using clay. How many
such cuboids will he need, to make a perfect cube.​

Answer 1

A cuboid of measurements 2cm, 5cm and 5cm will have a volume equal to 50 cm cube.

Volume of cube will be equal to X cm cube if it’s length is X.

Now in order to find no. of cuboids needed to form a cube, the sum of their lengths, breadths and heights must be equal to the length of Cube.

In case, she try’s forming a cube along the height, using 3 cuboids then she'll have dimensions as 5cm, 5cm and 6cm…again a cuboid as she didn't get the third dimension equal to 5 cm.

But, If she trys forming a cube using 5 cuboids she'll get a cuboid whose height will become 10 cm.

Now, if along the other 3 faces of this newly formed cuboid she places 5 more cuboids along each face, she'll get a total of 20 cuboids whose sides will be forming a cube having length equal to 10cm each!!

Therefore, she needs 20 cuboids of dimenions 5cm, 5cm and 2 cm in order to form a Cube.

ALTERNATIVE METHOD(EASY ONE):-

She has a Cuboid of volume 50cm cube.

Hence, the cube formed by these cuboids must be a multiple of 50.

THE FIRST CUBE THAT IS DIVISIBLE BY 50 IS 1000.

HENCE, number of cuboids required to form a cube is equal to 1000/50 = 20.

THEREFORE, THE ANSWER IS 20.

REFER THIS

Answer 2

Step-by-step explanation:

L.C.M. of 5 and 2 gives the dimension of the cube to be formed.

L.C.M. of 5 and 2 is 10.

Volume of cuboid =5×5×2=50cm

3

Volume of bigger cube = 10³= 1000

Number of cuboids required to make the bigger cube = (Volume of a cuboid)/(Volume of cube)

= 1000/50

=20