Answer:
[tex]136\pi in^2[/tex]
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
=[tex]2 \pi r h +\pi r^2[/tex]
=[tex]2 \pi (4)(12)+\pi(4)^2[/tex]
=[tex]96 \pi +16\pi[/tex]
=[tex]112\pi[/tex]
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 = [tex]\pi r l[/tex]
= [tex]\pi (4) (6)[/tex]
= [tex]24\pi[/tex]
Thus the total surface area = [tex]112\pi + 24\pi[/tex]
= [tex]136\pi in^2[/tex]
Hence the surface area of the tin man's head in terms of pi is [tex]136\pi in^2[/tex]
