Question:
a sphere of diameter 12 cm is dropped into a right circular cylinder vessel, partly filled with water. if the sphere is completely submerged in water, the water level in the vessel rises by 3*5/9 cm. find the diameter of the cylindrical vessel
Answer:
Given, diameter of the vessel = 12 cm
So, radius of the vessel = 12/2 = 6 cm
Now, volume of the sphere = (4/3)π r3
= (4/3)π*63
= (4/3)π*6*6*6
= 4*π*6*6*2
= 288π
Now, water displaced is equal to the volume of the sphere
Given, level of the water increased h = 3 (5/9) = 32/9
The shape of the given to be cylindrical.
Let r is the radius of the cylinder.
Now, volume of the water displaced = 288π
=> π r2 h= 288π
=> r2 * 32/9= 288
=> r2 = (288*9)/32
=> r2 = 9*9
=> r2 = 81
=> r = √81
=> r = 9
Hence diameter of the cylinder = 2r = 2*9 = 18 cm
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