Question

1. 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. lets do this in parts: part 1: how much of the bottom (cylinder) is covered in paint? part 2: how much of the top (cone) is covered in paint?

Explanation:

Part 1: Bottom (Cylinder)

Step 1: Area of the circular base of the cylinder

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 8\) mm.

$$A=\pi\times8^{2}=\pi\times64 = 64\pi$$

Part 2: Top (Cone - Lateral Surface Area)

Step 1: Lateral surface area of a cone

The formula for the lateral surface area of a cone is \(A=\pi rl\). Here, \(r = 8\) mm and \(l = 10\) mm (slant height).

$$A=\pi\times8\times10=80\pi$$

Answer:

Part 1: \(64\pi\) square millimeters.
Part 2: \(80\pi\) square millimeters.