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Question
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.
Solution
Given that, lots of spherical lead shots made from a solid rectangular lead piece.
∴ Number of spherical lead shots = `"Volume of solid rectangular lead piece"/"Volume of a spherical lead shot"` ...(i)
Also, given that diameter of a spherical lead shot i.e., sphere = 4.2 cm
∴ Radius of a spherical lead shot, r = `4.2/2` = 2.1 cm ...`[∵ "radius" = 1/2 "diameter"]`
So, volume of a spherical lead shot i.e., sphere
= `4/3 π"r"^3`
= `4/3 xx 22/7 xx (2.1)^3`
= `4/3 xx 22/7 xx 2.1 xx 2.1 xx 2.1`
= `(4 xx 22 xx 21 xx 21 xx 21)/(3 xx 7 xx 1000)`
Now, length of rectangular lead piece, I = 66 cm
Breadth of rectangular lead piece, b = 42 cm
Height of rectangular lead piece, h = 21 cm
∴ Volume of a solid rectangular lead piece i.e., cuboid
= I × b × h
= 66 × 42 × 21
From equation (i),
Number of spherical lead shots
= `(66 xx 42 xx 21)/(4 xx 22 xx 21 xx 21 xx 21) xx 3 xx 7 xx 1000`
= `(3 xx 22 xx 21 xx 2 xx 21 xx 21 xx 1000)/(4 xx 22 xx 21 xx 21 xx 21)`
= 3 × 2 × 250
= 6 × 250
= 1500
Hence, the required number of spherical lead shots is 1500.
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