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.)
(1 point)
Responses
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 cylinder, we need to find the lateral area (the rectangle) and the area of the two circles.
1. Lateral area = circumference of the base * height
Circumference = 2πr = 2*3.14*4.5 = 28.26 inches
Lateral area = 28.26 * 10.2 = 288.252 square inches
2. Area of the two circles = 2 * πr^2 = 2 * 3.14 * 4.5^2 = 127.105 square inches
Total surface area = Lateral area + Area of the two circles
Total surface area = 288.252 + 127.105 = 415.357 square inches
Therefore, Simone will need 415.42 square inches of patterned paper to cover the entire box.
Answer: 415.42 square inches