Q3 of 49 Page 1

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then calculate the rise of water level (in cm).

The rise of water level is due to the volume increase caused by the completely submerged sphere.

Volume increase in cylinder= Volume of sphere


We know that


Volume of cylinder= π r2h


Where, r= Radius of cylinder and h= Height of cylinder


Volume of sphere = (4/3) π R3


Where R= radius of sphere


So Volume of cylinder = Volume of sphere


⇒ π r2h = (4/3) π R3


⇒ (18)2 × h =(4/3) (9)3


⇒ h = 3 cm.


More from this chapter

All 49 →
1

In fig. 1, O is the center of a circle, AB is a chord and AT is the tangent at A. If ∠ AOB= 100°, then calculate ∠ BAT.

 2

In fig. 2, PA and PB are tangents to the circle with center O. If∠ APB=60°, then calculate∠ OAB.

 4

In which quadrant the point P that divides the line segment joining the points A (2, -5) and B (5, 2) in the ratio 2 : 3 lies?

 5

The angles of a triangle are in A.P., the least being half the greatest. Find the angles.