A pendant is formed using a cylinder and cone. Once assembled, as shown below, the pendant is painted. How many square millimeters are covered with paint? Express the answer in terms of π.
Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder
Area of the base of the cylinder = [tex] \pi r^{2} = 8^{2} \pi =64 \pi [/tex] Area of the cylinder 'wall' = width × length = [tex]12[/tex]×[tex]2r \pi [/tex]=[tex]12[/tex]×[tex]16 \pi [/tex]=[tex]192 \pi [/tex]
Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by [tex] \pirl[/tex] where [tex]l[/tex] is the slanted height of the cone
SA of cone = [tex] \pi (8)(10)=80 \pi [/tex]
Hence total painted surface area is [tex]80 \pi +192 \pi +64 \pi =336 \pi [/tex]
