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.

336π square millimeters
400π square millimeters
416π square millimeters
464π square millimeters

Answer 1

I don't have the diagram or the dimensions — can you upload the picture or give the radii and heights (and say which faces are painted)?

If you want to work it out yourself, here are the steps and formulas you'll need:

- If the cylinder and cone share the same base radius r and are glued together at that circular face, that shared circle is not painted.
- Painted area = lateral area of the cylinder + lateral area of the cone + any exposed circular base(s) (if the cylinder has a free circular face).
- Formulas:
- Cylinder lateral area = 2π r h_cyl
- Cone lateral area = π r s, where s is the slant height of the cone (s = sqrt(r^2 + h_cone^2))
- Circular base area (if exposed) = π r^2

Give me the dimensions or the picture and I’ll compute which of the four choices is correct.