Question

Ronit makes a cuboid of dimensions 5cm ,2cm and 5cm using clay .how many such cuboids will he need ,to make a perfect cube .

Answer 1

Answer:

Given -

• Dimensions of cuboid = 5 cm, 2 cm and 5 cm.

To find -

• Number of cuboids that ronit will need to make a perfect cube.

Solution -

Now, we have to find the LCM of the three sides of the cuboid to find the side of cube.

• LCM of 5,2,5 = 10

Now, the volume of the cuboid is -

2 × 5 × 5

→ 50 cubic metres.

Volume of new cube is -

10 × 10 × 10 cubic cm

→ 1000 cubic cm.

Therefore, Ronit need 1000 / 50

→ 20 cuboids to make a perfect cube.

Answer 2

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LONG METHOD(IN ORDER TO MAKE THE READER UNDERSTAND THE QUESTION):-

$\blue{\bold{\underline{\underline{Given:-}}}}$

• 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, he 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 he 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 he places 5 more cuboids along each face, he'll get a total of 20 cuboids whose sides will be forming a cube having length equal to 10cm each!!

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

ALTERNATIVE METHOD(EASY ONE):-

He 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.

$\bf\blue{Hope\ it\ helps.}$

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