plz help in this ques....
Answers
Radius of sphere = Radius of cylinder = 3.5 cm
When the sphere is in the cylinder, the height of water = Diameter of sphere
Height of cylinder = 3.5 * 2 = 7 cm
(1) .
Area of cylinder in contact with water = Area of Base of cylinder + 2*pi *r*h
= pi r ( r + 2h)
= 22*3.5 * 17.5 / 7
= 22*0.5*17.5
= 11 * 17.5
= 192.5 cm^2
2.)
Volume of water earlier, when the sphere is not poured in it = Volume of cylinder after pouring the sphere - Volume of sphere
= pi *3.5 *3.5 * 7 - 4 pi *3.5 * 3.5 *3.5 / 3
= pi * 3.5 * 3.5 ( 7 - 14/ 3)
= 22*3.5*3.5 * (21-14) / 7 * 3
= 22*0.5 * 3.5 * 7 /3
= 11*3.5 *7 / 3
= 77*3.5 /3
= 269.5 / 3
Volume of water in cylinder earlier = 269.5 / 3
=> pi * r^2 *h
=> 22*3.5 *3.5 *h / 7 = 269.5
=> h = 269.5 * 7 / 3.5 * 3.5* 22 * 3
=> h = 22*7 / 22 *3
=> h = 7/3
=> h = 2.3 cm (approx...)
Height of water in the cylinder earlier = 2.3 cm
Radius of cylinder = 3.5 cm
Radius of sphere = Radius of cylinder = 3.5 cm
When the sphere is in the cylinder, the height of water = Diameter of sphere
Height of cylinder = 3.5 * 2 = 7 cm
(1) .
Area of cylinder in contact with water = Area of Base of cylinder + 2*pi *r*h
= pi r ( r + 2h)
= 22*3.5 * 17.5 / 7
= 22*0.5*17.5
= 11 * 17.5
= 192.5 cm^2
2.)
Volume of water earlier, when the sphere is not poured in it = Volume of cylinder after pouring the sphere - Volume of sphere
= pi *3.5 *3.5 * 7 - 4 pi *3.5 * 3.5 *3.5 / 3
= pi * 3.5 * 3.5 ( 7 - 14/ 3)
= 22*3.5*3.5 * (21-14) / 7 * 3
= 22*0.5 * 3.5 * 7 /3
= 11*3.5 *7 / 3
= 77*3.5 /3
= 269.5 / 3
Volume of water in cylinder earlier = 269.5 / 3
=> pi * r^2 *h
=> 22*3.5 *3.5 *h / 7 = 269.5
=> h = 269.5 * 7 / 3.5 * 3.5* 22 * 3
=> h = 22*7 / 22 *3
=> h = 7/3
=> h = 2.3 cm (approx...)
Height of water in the cylinder earlier = 2.3 cm