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A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into 12 toys in the shape of a right circular cone mounted on a hemisphere.Find the radius of the hemisphere and total height of the toy.if the height of the cone is 3 time the radius . |
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Answer» Solution :Radius of the cylinder r= 6cm heigth of the cylinder ,h= 15 cm `therefoer`VOLUME of the cylinder `=pi r^h` `= (pixx 6xx 6xx 15) cm^3` `=(540 pi ) cm^3` Volume of 12 toys `=(540 pi)cm^3` `therefore`volume of 1 toy `=((540 pi)/(12))cm^3 =( 45 pi ) cm^3` Let the radius of each of the hemisphere and CONE be R cm Then , height of the cone `H= (3R) cm ` Volume of 1 toy = volume of the hemisphere + volume of the cone `= 2/3 pi R^3 + 1/3pi R^2 H` `=(2/3pi R^3 +1/3pi R^2xx3R) cm^3` `=((5 pi R^3)/(3))cm^3` `therefore (5pi R^3)/(3)= 45 pirArr R^3=(45 xx 3/5)=27 = 3^3 rArr R = 3` TOTAL height of the toy = (R + 3R) cm = 4 R cm `=(4 xx 3)` cm = 12 cm 
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