A right circular cone of diameter r cm and height 12cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12cm. If the cone is then removed, find the to which the water level will fall.

 adius of base of cone=r/2

radius of base ofcylinder=r

height of cone=12cm

h of water before cone ws tkn out=12cm

thus, vol of water left in cylinder aftr cone is tken out=vol of water - vol of cone

=pi x r^2 x 12 - 1/3x pi x(r/2)^2 x 12

=pi x r^2x11

u cn observe that 11 is present height (or "h") of the water(refer cylinder 's volume formula)

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Let r and  be the radius of base of the cylinder and cone respectively.

Height of the water in the cylinder = 12 cm

Height of the cone, h = 12 cm

Volume of water

= (12 π r 2 – π r 2) cm3

= 11 π r 2 cm3

Let the height of water in the cylinder be h' when the cone is removed.

Volume of water = 11 π r 2 cm3

∴ πr 2 h' = 11 π r 2

⇒ h' = 11

Thus, the level of water in the cylinder is 11 cm.

not even expert can say it wrong

-by yudhik

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Great Yudhik

  • -6
answer is 1 cm
  • -8
Thanks yudhik this answer helped me a lot
  • -4
Y is pie r^2 subtracted from 12pie r^2
  • -11
base radius of cone be r 
base radius of cylinder be r/2
height of cone & cylinder is 12 cm
volume of water left = volume of water - volume of cone 
                                  = pi r^2*h - 1/3 pi r^2*h
                                  = pi r^2*12 - 1/3 pi (r/2)^2 *12
                                 = 12 pi r^2 - pi r^2
                                  =11 pi r^2 cm^3
height of water in cylinder be h when the cone is removed 
          volume of water = 11 pi r^2 cm^3

thus, the level of water in the cylinder = 11 cm
  • 1
You forgot to subtract original - new height
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This is ans

  • 70
Yudhik subtract 12-11 at last
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Nice yudhvik
  • -4
Why we substrated at last
  • -1
Hope this help

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