area of right circular cylinder

Question

The diameter of the base of a right circular cylinder is 18.2 cm and the ratio of the area of its curved surface to the area of the base is 15:13. Find the total surface area of the cylinder?

Answer 1

Area of curved surface = (circumference)(height) = 2πrh

Area of base = πr²

 

So, 15/13 = 2πrh/(πr²) = 2h/r

 

Cross multiply to get 15r = 26h

 

                                   h = (15/26)r = (15/26)(9.1) = 5.25

 

Surface area of cylinder = 2(area of base) + area of side

 

                                     = 2πr² + 2πrh

 

                                     = 2π(9.1)² + 2π(9.1)(5.25)

 

                                     = 261.17π

 

                                     ≈ 820.5 cm²