Question
Download Solution PDFHow many spherical lead shots each of radius 2.1 cm can be obtained from a solid rectangular lead piece with dimensions 84 cm, 77 cm and 63 cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
Spherical lead shots of radius 2.1 cm.
Rectangular lead piece of dimension 84 cm, 77 cm, 63 cm.
Formula used :
Volume of sphere = 4/3πr3
Volume of cuboid = l × b × h
Calculation :
According to question,
Let the number of spherical lead shots be n.
⇒ 84 × 77 × 63 = n × 4/3 × 22/7 × 2.1 × 2.1 × 2.1
⇒ 21 × 77 × 63= n × 1/3 × 22/7 × 21/10 × 21/10 × 21/10
⇒ 21 × 77 × 63 = n × 22 × 21/10 × 21/10 × 1/10
⇒ 77 × 63 = n × 22 × 21/1000
⇒ 7/2 × 63 = n × 21/1000
⇒ n = 7/2 × 3000
⇒ n = 7 × 1500
⇒ n = 10500
∴ The correct answer is 10500.
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