The volume of a cylinder is given by V=πr^2h . If each of the radius and height of the cylinder increases by 2%, what is the increase in its volume and its surface area?

1 Answer
Nov 30, 2017

Increase in volume is 0.06*pir^2h (6%) and increase in surface area is 0.04*2pi r(r+h)(4%)

Explanation:

Let radius and height of original cylinder be r and h respectively.

2% increase means new radius and height will be 1.02r,1.02h

respectively. Volume of original cylinder is V_1= pi r^2h and

volume of larger cylinder is V_2= pi(1.02r)^2*1.02h

Increase in volume is V_2-V_1= pi(1.02r)^2*1.02h-pi r^2h or

V_2-V_1= pi r^2h(1.02^3-1)~~pir^2h*0.06(2dp)

cubic.unit. Surface area of original cylinder is S_1= 2 pi r(r+h) and

surface area of larger cylinder is S_2= 2 pi*1.02r(1.02r+1.02h)

=2 pi *1.02^2*r(r+h) .Increase in surface area is

S_2-S_1= 2 pi r(r+h)(1.02^2-1)=2pi r(r+h)*0.04 .

Increase in volume is 0.06*pir^2h (6%)

and increase in surface area is 0.04*2pi r(r+h)(4%) [Ans]