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Question
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.
Solution
Given that, lots of spherical lead shots made out of a solid cube of lead.
∴ Number of spherical lead shots = `"Volume of a solid cube of lead"/"Volume of a spherical lead shot"` ...(i)
Given that, a diameter of a spherical lead shot i.e., sphere = 4 cm
⇒ Radius of a spherical lead shot (r) = `4/2`
r = 2 cm ...[∵ Diameter = 2 × Radius]
So, volume of a spherical lead shot i.e. sphere
= `4/3 pi"r"^3`
= `4/3 xx 22/7 xx (2)^3`
= `(4 xx 22 xx 8)/21 "cm"^3`
Now, since edge of a solid cube (a) = 44 cm
So, volume of a solid cube = (a)3
= (44)3
= 44 × 44 × 44 cm3
From equation (i),
Number of spherical lead shots
= `(44 xx 44 xx 44)/(4 xx 22 xx 8) xx 21`
= 11 × 11 × 21
= 121 × 21
= 2541
Hence, the required number of spherical lead shots is 2541.
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