Question

Abhay wants to create a cube using cuboid of dimensions 2 cm x 3 cm x 5 cm. How many such cuboid will he require to make the smallest perfect cube.​

Answer 1

Volume of each cuboid = 12×8×3=288cm3

LCM of 12,8 & 3 is 24. Therefore minimum edge length of cube formed will be 24 cm.

Volume of cube = n× volume of 1 cuboid   [n= number of cuboid ]

⇒(24)3=n×288

⇒n=28824×24×24=48

Hence, number of cuboids =48

Answer 2

Answer:

20 cuboids

Step-by-step explanation:

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Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Answer

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Hint- Here, we will proceed by finding the volume of one cuboid by the formula i.e., Volume of the cuboid = (Length of the cuboid)×(Breadth of the cuboid)×(Height of the cuboid) and then we will find the volume of the biggest cube using the formula i.e., Volume of the cube = (Side of the cube)3. To find the number of cuboids required to form the biggest cube is given by dividing the volume of the biggest cube by the volume of the cuboid.

Complete step-by-step answer:

Given, Length of the cuboid of plasticine = 5 cm

Breadth of the cuboid of plasticine = 2 cm

Height of the cuboid of plasticine = 5 cm

As we know that volume of the cuboid is given by

Volume of the cuboid = (Length of the cuboid)×(Breadth of the cuboid)×(Height of the cuboid)

⇒Volume of the cuboid of plasticine = 5×2×5 = 50 cm3

Cube is a special form of cuboid in which length, breadth and height are equal i.e., all the dimensions of a cube are equal in measure.

Dimension (or side) of the biggest cube which can be formed by joining some cuboids each of sides 5 cm, 2 cm, 5 cm is equal to the LCM of the sides of the cuboid

i.e., Side of the biggest cube = LCM of 5,2,5 = 10