If the radius and height of the cone both are increased by 10%, then volume and surface area of cone is increased by:

Explanation

Let radius of cone is `r` and height is `h`.

Then, radius after increase ` = r+10/100 = 1.1r`

Similarly, height after increase `= 1.1h`

Initial surface area of cone`(S_1) = pir(r+l)= pir^2+pirsqrt(h^2+r^2)`

Initial volume of cone `(V_1) = 1/3pir^2h`

Surface area after increase `(S_2) = pi(1.1r)^2+pi(1.1r)sqrt((1.1h)^2+(1.1)r^2)`

`S_2 = (1.1)^2(pir^2+pisqrt(h^2+r^2)) = 1.21 S_1`

`:. %` increase in Surface area `= (1.21S_1-S_1)/S_1**100 = 21%`

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