Question

the diameter of a cylindrical box of CDs is 5 inches. The height of the box is 4 inches. Whuch measurement is closest to the total surface area of the CD box in square inches

Answer 1

to find area you simply multiply 5 and 4 which is 20

Answer 2

The equation for the surface area of cylinder is $SA = 2 \pi rh+2 \pi r^{2}$, where SA = surface area, r = radius, and h = height.

To help you remember this equation, remember that the surface area is the total area of all the surfaces of a shape. A cylinder is made up of two circles and a long rectangle that creates the body of the cylinder (see picture). The surface area is thus the area of the two circles ($2 \times \pi r^{2}$) plus the area of the rectangle ($2 \pi r \times h$), which has a width of 2πr (aka the circumference of a circle) and a height of h. 

Back to the problem:
You are told that the diameter of the cylinder is 5in. Remember that the diameter = 2r (2 times the radius). That means the radius, r = 5/2 = 2.5 in. You are also told the height, h = 4in. Plug these values into the equation for the surface area of a cylinder:
$SA = 2 \pi rh+2 \pi r^{2} \\ SA = 2 \pi (2.5)(4)+2 \pi (2.5)^{2}\\ SA \approx 102.1 \: in^{2}$

The surface area is about 102.1 square inches.