7.5 Conversion of Solids from one shape to another with no change in Volume · Part 2

height cm and base radius cm, having a hemispherical cap. Find the number of cones needed to empty the container. Solution Let h and r be the height and radius of the cylinder respectively. Given that, h = cm, r = cm Volume of the container V r h = p cubic units. × × × Let, r = cm, h = cm be the radius and height of the cone. Also, r = cm is the radius of the hemispherical cap. Volume of one ice cream cone = (Volume of the cone + Volume of the hemispherical cap) r h × × × × × × ) = Number of cones = volume of the cylinder volume of oneice cream cone Number of ice cream cones needed = × × × = Thus ice cream cones are required to empty the cylindrical container. Activity The adjacent figure shows a cylindrical can with two balls. The can is just large enough so that two balls will fit inside with the lid on. The radius of each tennis ball is cm. Calculate the following (i) height of the cylinder. (ii) radius of the cylinder. (iii) volume of the cylinder. (iv) volume of two balls. (v) volume of the cylinder not occupied by the balls. (vi) percentage of the volume occupied by the balls. Exercise . . An aluminium sphere of radius cm is melted to make a cylinder of radius cm. Find the height of the cylinder. . Water is flowing at the rate of km per hour through a pipe of diameter cm into a rectangular tank which is m long and m wide. Find the time in which the level of water in the tanks will rise by cm. . A conical flask is full of water. The flask