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. How much paper will Simone need to cover the entire box? (Use 3.14 for π.)
74.16 square inches
74.16 square inches
206.55 square inches
206.55 square inches
415.42 square inches
415.42 square inches
648.57 square inches
To find the surface area of the cylindrical storage box, we need to calculate the lateral surface area and the surface area of the top and bottom.
Lateral surface area = 2πrh
= 2 * 3.14 * 4.5 * 10.2
= 289.08 square inches
Surface area of the top and bottom = 2πr^2
= 2 * 3.14 * 4.5^2
= 127.305 square inches
Total surface area = Lateral surface area + Surface area of top and bottom
= 289.08 + 127.305
= 416.385 square inches
Therefore, Simone will need 415.42 square inches of paper to cover the entire box.