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How many cubes of side 8 cm can be formed by melting a cuboid of length 24 cm, breadth 16 cm and height 16 cm?
Question

How many cubes of side 8 cm can be formed by melting a cuboid of length 24 cm, breadth 16 cm and height 16 cm?

A.

14

B.

16

C.

10

D.

12

Correct option is D

Given:

Cuboid Dimensions:

  • Length = 24 cm
  • Breadth = 16 cm
  • Height = 16 cm

Cube Side Length = 8 cm

Formula Used:

The volume remains the same after melting and reshaping.
Thus, the number of small cubes that can be formed is:

Number of cubes=Volume of the cuboidVolume of one cube\text{Number of cubes} = \frac{\text{Volume of the cuboid}}{\text{Volume of one cube}}​​

Volume of cuboid = Length × Breadth × Height

Volume of cube = Side³

Solution:

Calculate the volume of the cuboid:

24×16×16=6144 cm324 \times 16 \times 16 = 6144 \text{ cm}^3​​

Calculate the volume of one cube:

83=512 cm38^3 = 512 \text{ cm}^3​​

Find the number of cubes:

6144512=12\frac{6144}{512} = 12

Option (d) is right.

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