Question

Parikshit makes a cuboid of plastic of sides 5cm, 2cm, 5cm. How many such cuboids will be needed to form a cube?
$
  {\text{A}}{\text{. 30}} \\
  {\text{B}}{\text{. 15}} \\
  {\text{C}}{\text{. 20}} \\
  {\text{D}}{\text{. 25}} \\
$

Answer 1

Hint: To find the number of cuboids, we use the formula of volume of cube, which is given as, Volume of cube = volume of cuboid x number of cuboids.Find the length of cube by taking L.C.M of length of sides of cuboid then, find the volume of cube and equate it into the formula we get number of cuboids needed to form cube.

Complete step-by-step answer:
Given Data, the sides of the cuboid 5cm, 2cm and 5cm.
Let length of the cuboid l = 5cm
Let breadth of the cuboid b = 5cm
Let height of the cuboid h = 2cm

⟹Volume of the cuboid = l x b x h = 5 x 5 x 2
                                             = 50 ${\text{c}}{{\text{m}}^3}$

Volume of cube = volume of cuboid x number of cuboids
 Let the length of the side of a cube be a cm.
Volume of the cube = ${{\text{a}}^3}{\text{c}}{{\text{m}}^3}$

So, ${{\text{a}}^3}$ = 50${\text{c}}{{\text{m}}^3}$ x number of cuboids.

The least length of the cube is given as the LCM of the lengths of cuboid sides. The LCM of 5, 5 and 2 is 10. Hence, the least length of the cube is 10 cm as the dimensions of the cuboid are 5cm, 2cm and 5cm. The length of all the sides of the cube are equal.

${10^3}$ = 50 x Number of cuboids
Number of cuboids = $\dfrac{{1000}}{{50}}$

Hence, Number of cuboids = 20

Note: In order to solve this type of question the key is to identify the least length of the side of the cube and compute it using its formula. The length of all the sides of the cube are equal. Since the cube is to be formed by the cuboids the least length of the side of a cube will be 10cm.