Question

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?

Answer 1

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]