Q10 of 67 Page 195

How many spherical lead shots each 4.2 cm in diameter can be obtained from a rectangular solid of lead with dimensions 66 cm, 42 cm and 21 cm.

Diameter of spherical lead shot = 4.2 cm


⇒ radius of spherical lead shots = r = = 2.1 cm


Length of solid lead = l = 66 cm


Breadth = b = 42 cm


Height = h = 21 cm


Volume of sphere = πr3


Volume of rectangular lead = lbh


As the spherical lead shots are obtained from rectangular lead volume remains same


Let n spherical lead shots are made


⇒ n × πr3 = lbh


Substituting values


⇒ n × × × 2.13 = 66 × 42 × 21


⇒ n × × × 2.12 = 3 × 42 × 10


⇒ n × × × 2.1 = 3 × 20 × 10


⇒ n × × 0.3 = 600


⇒ n × 4 × 0.1 = 600


⇒ n × 4 × = 600


⇒ n × 4 = 6000


⇒ n = 1500


Therefore, 1500 spherical lead shots are formed


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