If the diameter of a right circular cylinder is decreased by 5% ,then find the percentage increase in its height so that its volume remains same.
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Let's say the length of radius be x
Now we know that if diameter will decrease by 5% the radius will also decrease by 5%
Let's say initial volume was 100
we know
Volume of cylinder =πr^2h
100=πx^2*h
case 2
Volume of cylinder =100
π(x-0.05x)^2(h+y)=100
dividing equation 1 and 2
x^2*h/(0.95x^2)(h+y)=1
x^2/0.9025x^2=(h+y)/h
1.108=(h+y)/h
1.108h=h+y
y=0.108h
%of h =(0.108h/h)*100
=10.8%
The percentage increase is 10.8 %
sry if there was any mistake
This is the theoretical method
Still if ur looking for a mcq approach assumption of values would have been faster
Now we know that if diameter will decrease by 5% the radius will also decrease by 5%
Let's say initial volume was 100
we know
Volume of cylinder =πr^2h
100=πx^2*h
case 2
Volume of cylinder =100
π(x-0.05x)^2(h+y)=100
dividing equation 1 and 2
x^2*h/(0.95x^2)(h+y)=1
x^2/0.9025x^2=(h+y)/h
1.108=(h+y)/h
1.108h=h+y
y=0.108h
%of h =(0.108h/h)*100
=10.8%
The percentage increase is 10.8 %
sry if there was any mistake
This is the theoretical method
Still if ur looking for a mcq approach assumption of values would have been faster
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