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A cuboid with dimensions 24 cm × 16 cm × 10 cm is melted to form smaller cubes with sides of 4 cm. Determine the number of cubes that can be formed.
Question

A cuboid with dimensions 24 cm × 16 cm × 10 cm is melted to form smaller cubes with sides of 4 cm. Determine the number of cubes that can be formed.

A.

58

B.

62

C.

64

D.

60

Correct option is D

Given
Dimensions of the cuboid = 24 cm × 16 cm × 10 cm
Side of the smaller cube = 4 cm
Formula Used
Volume of a cuboid=Length×Breadth×Height Volume of a cube=Side3 Number of cubes=Volume of CuboidVolume of one Cube \text{Volume of a cuboid} = \text{Length} × \text{Breadth} × \text{Height} \\\ \\\text{Volume of a cube} = \text{Side}^3 \\\ \\\text{Number of cubes} = \frac{\text{Volume of Cuboid}}{\text{Volume of one Cube}} \\\ \\​​
Solution
Volume of the cuboid=24×16×10=3840cm3 Volume of one small cube=4×4×4=64cm3 Number of cubes=384064=60 \text{Volume of the cuboid} = 24 × 16 × 10 = 3840 cm^3 \\\ \\\text{Volume of one small cube} = 4 × 4 × 4 = 64 cm^3\\\ \\\text{Number of cubes} = \frac{3840}{64} = 60\\\ \\​​
Final Answer
So the correct answer is (d)

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