Algebra -Direct proportion - Linear,nonlinear

Algebra -Direct proportion - Linear,nonlinear

Postby Chathurangi » Sat Jul 21, 2018 11:45 am

Cylinder P has radius xcm and is filled with water to a depth of dcm.
This water is poured in to cylinder Q and filles it to a depth of 3dcm.What is the radius of cylinder Q?
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Re: Algebra -Direct proportion - Linear,nonlinear

Postby HallsofIvy » Mon Dec 23, 2019 12:28 am

A cylinder with radius r and height h has volume [tex]\pi r^2h[/tex] so a cylinder of radius x cm and height d cm has volume [tex]\pi x^2d[/tex] cubic centimeters. That is the volume of water filling that cylinder. A cylinder of radius r and height 3 cm has volume [tex]\pi r^2(3)= 3\pi r^2[/tex]. If the water fills the second cylinder to that height then we must have [tex]3\pi r^2= \pi x^2d[/tex]. Solve that equation for r.

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