Question

the radius of the base of right circuler cylinder increase by 75percent &height is decreased by 50percent .find the percent increase & decrease in curve surface .

Answer 1

Initial curved surface area of cylinder = 2πr h
new radius, R = r + 75% of r = 1.75 r
new height, H = h - 50% of h = 0.5 h
new curved surface area =2πRH = 2π×(1.75 r)×(0.5 h)
                                        = 2πrh ×0.875 
area decreased = 2πrh - 2πrh ×0.875 =  0.125 ×2πrh
percent decrease = [(0.125×2πrh)/(2πrh)]×100 = 12.5%