Each of the radius and the height of a right circular cylinder is both increased by 10% . Find the % by which the volume increases.
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Let radius be r and height be h.
=Increased radius=r+r×1/100=r+r/100=101r/100=1.01r
=Increased height=h+h×1/100=h+h/100=101h/100=1.01h
=Change in volume=New volume- Original volume
=(22/7×(1.01r)²×1.01h) - (22/7r²h)
22/7×1.201r²×1.01h - 22/7r²h
1.030301r²h-r²h(22/7)
1.030301 - 1(22/7r²h)
0.030301(22/7r²h)
% change=change in volume/original volume×100
0.030301(22/7r²h)/22/7r²h=0.030301×100=3.03%
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