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
648.57 square inches
there are optons
To find the surface area of the entire box, we need to find the lateral surface area as well as the surface areas of the top and bottom circles.
Lateral Surface Area = 2πrh
= 2 * 3.14 * 4.5 * 10.2
= 289.08 square inches
Surface Area of Top and Bottom Circles = 2πr^2
= 2 * 3.14 * 4.5^2
= 127.05 square inches
Total Surface Area = Lateral Surface Area + 2(Top and Bottom Circles)
= 289.08 + 2(127.05)
= 289.08 + 254.1
= 543.18 square inches
Therefore, Simone will need 543.18 square inches of patterned paper to cover the entire box. None of the given options match this result, it seems there may be an error in the calculations.