Simone has a red cylindrical storage box that she would like to decorate with patterned paper. The radius of the box is 4.5 inches and the height is 10.2 inches. The cylinder’s net is shown below. How much paper will Simone need to cover the entire box? (Use 3.14 for π.)

Answer 1

To find the total surface area of the cylinder, we need to find the area of the two circles at the top and bottom, and the area of the rectangle wrapped around the sides.

1. Area of the top circle:
A = πr^2
A = 3.14 * (4.5)^2
A = 3.14 * 20.25
A = 63.585 square inches

2. Area of the bottom circle:
A = πr^2
A = 3.14 * (4.5)^2
A = 3.14 * 20.25
A = 63.585 square inches

3. Area of the side rectangle:
A = 2πrh
A = 2 * 3.14 * 4.5 * 10.2
A = 286.74 square inches

Now, add up the three areas to find the total surface area of the cylinder:
Total surface area = 63.585 + 63.585 + 286.74
Total surface area = 413.91 square inches

Therefore, Simone will need 413.91 square inches of patterned paper to cover the entire box.