Atin man has a head that is a cylinder with a cone on top. the height of the cylinder is 12 inches and the slant height of the cone is 6 inches. the radius of both the cylinder and the cone is 4 inches. what is the surface area of the tin man's head in terms of pi?
a) 136π in²
b) 152π in²
c) 168π in²
d) 172π in²

i already figured out the surface area of the cylinder (128π i just don't know how to include the cone into the equation. i'm stumped..

Step-by-step explanation:

Height of cylinder = 12 inches

Radius of cylinder = 4 inches

Since we are given that A tin man has a head that is a cylinder with a cone on top.

So, Surface area of cylinder = Curved surface area of cylinder + Area of one base

                                              =

                                              =

                                              =

                                              =

Cone is joined on the top of the cylinder

So, we are required to find the lateral surface area of cone .

Slant height of cone = 6 inches

Radius of cone = 4 inches

So, Lateral surface area of cone =

                                                      =

                                                      =

Thus the total surface area =

                                              =

Hence the surface area of the tin man's head in terms of pi is

the answe i =−n+5