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 (pi).
(\bigcirc) (336pi) square millimeters
(\bigcirc) (400pi) square millimeters
(\bigcirc) (416pi) square millimeters
(\bigcirc) (464pi) square millimeters

Explanation:

Step1: Identify painted surfaces

We need the lateral (curved) surface area of the cone, lateral surface area of the cylinder, and area of the cylinder's base. The cone's base and cylinder's top are glued, so they are not painted.

Step2: Calculate cone lateral area

Formula: $\pi r l$
$r=8$ mm, $l=10$ mm
$\pi \times 8 \times 10 = 80\pi$

Step3: Calculate cylinder lateral area

Formula: $2\pi r h$
$r=8$ mm, $h=12$ mm
$2\pi \times 8 \times 12 = 192\pi$

Step4: Calculate cylinder base area

Formula: $\pi r^2$
$\pi \times 8^2 = 64\pi$

Step5: Sum all painted areas

$80\pi + 192\pi + 64\pi = 416\pi$

Answer:

416π square millimeters