two spherical cylindrcal balls are dropped into the water contained in a cylindrical vessel and the balls are completely submerged. the water level is raised by 6cm. if diameter of 1 sphere is twice the other and the diameter of a cylindrical vessel is 8 cm find the diameter of the two sphere immersed
Answers
Given : two spherical cylindrcal balls are dropped into the water contained in a cylindrical vessel and the balls are completely submerged. the water level is raised by 6cm . diameter of 1 sphere is twice the other and the diameter of a cylindrical vessel is 8 cm
To find : diameter of the two sphere immersed
Solution:
Diameter of cylindrical vessel = 8 cm
Radius of cylindrical vessel = 8/2 = 4 cm
water level is raised by 6cm
Volume of water Displaced = πR²h
= π (4)² 6
= 96 π cm³
Radius of one sphere = R cm
Radius of other sphere = 2R cm
Volume of sphere = (4/3) π ( Radius)³
Volume of both spheres = (4/3)πR³ +(4/3)π(2R)³
= (4/3)πR³ +(4/3)π8R³
= (4/3)π9R³
= 12πR³
Volume of both spheres = volume of water displaced
12πR³ = 96 π cm³
=> R³ = 8
=> R = 2 cm
Diameter = 2 * Radius
Radius of one sphere = 2 cm => Diameter of one sphere = 4 cm
Radius of other sphere = 4 cm => Diameter of other sphere = 8 cm
the diameter of the two sphere immersed = 4 cm & 8 cm
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