How to solve these four questions of surface area of revolution?

1.

The surface figured, which is part of a right-circular cone, is called a frustrum. But it kind of looks like a fez. frustrum fez S - R - If the radii of the top and bottom are r and R and the slant height is s (note lower case s), then the surface area of the frustrum (not including the base or top) is A = So to make a fez with top radius 10 cm, bottom radius 11 cm and slant height 16 cm requires + squared cm of felt. Note: the Maple syntax for r is Pi and to make a fez requires enough felt to cover the frustrum and the top circle.The function f(x) = e for x = 0 to co can be rotated about the x axis to form a surface of revolution S, which looks like a traffic cone (if you chop off the infinite tail!). Surface of revolution S Traffic Cones The Duke of Wellington, by Patrick Morgan CC-BY 2.0In general, the surface area of a surface of revolution about the 9; -axis of a curve described by y = f(:c) with a S a: S b, is given by the formula b , 2 A=f27rf(m),/1+ (f (33)) d3. 0, Find the surface area of the surface 8: This integral may help with your working, 1 f1/1+u2du= %(+m(+1)). 0 Note: the Maple notation for 1r is Pi. The Maple syntax for log(a:) is ln (x) . If you would like to know more, click here to see a video that nicely demonstrates the process by which surfaces of revolution are formed. | A curve can also be specified using polar co-ordinates and then rotated about the x-axis. Consider the curve specified by r = 1 where 0