Last updated at May 29, 2018 by Teachoo

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Ex 13.2, 5 A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. Number of lead shots = (๐๐๐๐ข๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐๐๐๐ค๐ ๐๐ข๐ก)/(๐๐๐๐ข๐๐ ๐๐ 1 ๐๐๐๐ ๐ โ๐๐ก) Volume of water flown out Volume of water flown out = 1/4 of volume of cone Given radius of cone = r = 5 cm height of cone = h = 8 cm Volume of cone = 1/3 ๐๐^2 โ = 1/3ร22/7ร5ร5ร8 = 4400/21 cm3 Volume of water flown out = 1/4 ร Volume of cone = 1/4 ร 4400/21 = 1100/21 cm3 Volume of 1 lead shot Lead shot is in from of sphere with Radius = r = 0.5 cm Volume of 1 lead shot = Volume of sphere = 4/3 ฯr3 = 4/3ร22/7ร(0.5)3 = 11/21 cm3 Now, Number of lead shots = (๐๐๐๐ข๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐๐๐๐ค๐ ๐๐ข๐ก)/(๐๐๐๐ข๐๐ ๐๐ 1 ๐๐๐๐ ๐ โ๐๐ก) = (1100/21)/(11/21) = 1100/21 ร 21/11 = 100 Hence there are 100 such lead shots.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.