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Q.

Parikshit makes a cuboid of plastic on the sides 5cm, 2cm, 5cm. How many such cuboids will be needed to form a cube?

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a

30

b

15

c

20

d

25

answer is C.

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Detailed Solution

Concept- The volume of cube formula, which reads: Volume of cube = volume of cuboid x number of cuboids, is used to determine the number of cuboids. Find the volume of the cube and plug it into the formula to get the number of cuboids required to construct the cube. Next, find the length of the cube by taking L.C.M. of the length of the cuboid's sides.
Given the data, the cuboid's sides are 5 cm, 2 cm, and 5 cm.
Let the cuboid's length be 5 cm.
Assume that the cuboid's width is 5 cm.
Let the cuboid's height be 2 cm.
The cuboid's volume is equal to

50 c m^{3} (l x b x h = 5 x 5 x 2)

Volume of a cube equals the sum of the volumes of all its cuboids.
Let each cube side measure one centimeter in length.
Cube volume is equal to

a^{3}

c

m^{3}

As a result,

a^{3}

= 50c

m^{3}

x cuboids.
The LCM of the cuboid side lengths is used to determine the cube's smallest length.

10, or the LCM of 5, 5, and 2 .

As a result, the cube's shortest length is 10 cm, and the
since the cuboid's measurements are

5, 2, and 5 cm .

The cube's sides are all the same length.

10^{3}

= Number of Cuboids x 50

\frac{1000}{50}

cuboids are present.
Therefore, there are 20 cuboids.
Hence, the correct option is 3.
ExamType: CBSE

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