if cylinders radius is increased by 50%,then by how much %height should decrease so that volume remains same
Answers
Let the radius of the original cylinder =r cm and
Height=h cm
Original volume=πr2h
New Radius after increase = 150/100r=3/2r
New height after decrease=80/100h=4/5h
Now, new volume of the cylinder=π×(3r/2)2×4/5h=9πr2/5h
% increase=Changeinvolume__ =dfrac9πr2 5h-pir2h__ ×100=4πr2__ h
Original volume πr2h 5__
πr2h ×100=4/5×100=80%
Let assume that
Radius of cylinder be r units
Height of cylinder be h units
We know, Volume (V) of cylinder of radius r and height h is given by
Now, given that
Radius is increased by 50 % of the original radius.
So,
Let assume that height of cylinder be decreased by x %.
So,
So, Volume V' of radius r' and height h' is given by
According to statement,
On substituting the value of r' and h', we get
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