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How many lead shots, each measuring 3 mm in diameter, can be produced using a cuboid of dimensions $12 c m × 11 c m × 9 c m$ ?

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84000

85000

86000

87000

answer is A.

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Detailed Solution

It is given that the lead shot’s diameter is 3 mm.
Therefore, the lead shot’s radius is,

32 mm = 0.3 2 cm

[10 mm = 1 cm]
Also, given that the dimension of the cuboid is

We know that the volume of the sphere is

43 π r 3,

where r is the radius of the sphere.
The volume of a cuboid is

where

is length,

is the breadth, and

is height.

∴ Number of lead shots = Volume of the cuboid Volume of 1 lead shot = 12 × 11 × 9 43 × 227 × 0.3 2 3

= 12 × 11 × 9 43 × 227 × 0.027 8

= 84000

Therefore, the number of lead shots is 84000.
Hence, option (1) is correct.

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