Question

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.

Answer 1

Explanation:

336pi

Answer 2

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 =
`\pi r^(2) = 8^(2) \pi =64 \pi`
Area of the cylinder 'wall' = width × length =
`12`×
`2r \pi`=
`12`×
`16 \pi`=
`192 \pi`

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
`\pirl` where
`l` is the slanted height of the cone

SA of cone =
`\pi (8)(10)=80 \pi`

Hence total painted surface area is
`80 \pi +192 \pi +64 \pi =336 \pi`