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(B) The volume of water displaced is equal to the volume of the sphere submerged in the water.Radius of the sphere $(r_s)$ = $30 \ cm$.Radius of the c

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$22$

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(B) The volume of water displaced is equal to the volume of the sphere submerged in the water.Radius of the sphere $(r_s)$ = $30 \ cm$.Radius of the cylindrical vessel $(r_c)$ = $	ext{Diameter} / 2 = 80 \ cm / 2 = 40 \ cm$.Let the rise in water level be $x \ cm$.The volume of the displaced water in the cylinder is given by $\pi 	imes (r_c)^2 	imes x$.The volume of the sphere is given by $\frac{4}{3} \pi 	imes (r_s)^3$.Equating the two volumes: $\pi 	imes (40)^2 	imes x = \frac{4}{3} \pi 	imes (30)^3$.$1600 	imes x = \frac{4}{3} 	imes 27000$.$1600 	imes x = 4 	imes 9000$.$1600 	imes x = 36000$.$x = 36000 / 1600 = 360 / 16 = 22.5 \ cm$.Thus,the level of water rises by $22.5 \ cm$.

$A$ sphere of $30 \ cm$ radius is dropped into a cylindrical vessel of $80 \ cm$ diameter,which is partly filled with water. If its level rises by $x \ cm$,find $x$ (in $cm$). (in $.5$)

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