Question

Anita makes a cuboid of sides of 4cm,3cm and 3cm.how many such cuboids will she need to form a cube?​

Answer 1

Answer:

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.

Answer 2

let us assume she needs n cuboids

so

volume of cuboid *no of cuboid =volume of cube

4*3*3*n=a^3

so n=4*4*3 to balance out the equation

so

48 such cubes will be required.

and the side of each cube will be 12cm.