This pencil cup is made out of plastic. It is 5 inches tall and has a radius of 1.75 inches. How many square inches of plastic were used to make the cup

To make the cup 64.57 square inches of plastic were used.

Step-by-step explanation:

A cup has the format of a cylinder with a open top. The surface area of the cup is given by the area of it's base (a circle) and the area of it's walls, wich can be seen as rectangle where the width is the length of the circle at the base and the height is the height of the cylinder. So we have:

area of the base = pi*r^2 = 3.14 * (1.75) ^2 = 3.14*3.0625 = 9.616 square inches

area of the walls = 2*pi*r*h = 2*3.14 * (1.75) * 5 = 54.95 square inches

surface area of the cup = area of the base + area of the walls = 9.616 + 54.95

surface area of the cup = 64.57 square inches

To make the cup 64.57 square inches of plastic were used.