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How many small cubes with an edge of 20 cm each can be just accommodated in a cubical box of 2 m edge?

A) 10
B) 100
C) 1000
D) 10000

Answer :

Final answer:

A total of 1000 small cubes with an edge of 20 cm can be accommodated in a large cubical box with an edge of 2 meters.

The correct option is, 1000, which is, (C).

Explanation:

To find out how many small cubes with an edge of 20 cm each can fit in a cubical box of 2 m edge, we need to calculate the volume of the large cubical box and divide it by the volume of one of the small cubes.

The edge of the large cubical box is 2 meters, which is equivalent to 200 cm (1 m = 100 cm). The volume of the large cubical box (Vlarge) is therefore:

Vlarge = edge3 = 200 cm x 200 cm x 200 cm = 8,000,000 cm3

Similarly, the volume of one small cube (Vsmall) with an edge length of 20 cm is:

Vsmall = edge3 = 20 cm x 20 cm x 20 cm = 8,000 cm3

To find the number of small cubes that can fit inside the large cube, we divide the large cube's volume by the small cube's volume:

Number of small cubes = Vlarge / Vsmall = 8,000,000 cm3 / 8,000 cm3 = 1000

Therefore, 1000 small cubes can be accommodated in the large cubical box. The correct answer is C) 1000.

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