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.)
please pick from the given options using the 7th grade formula sheet
(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
To find the surface area of the entire box, we need to find the area of the two circles at the ends of the cylinder and the area of the rectangle that wraps around the cylinder.
1. Area of the two circles: 2 * π * radius^2
= 2 * 3.14 * 4.5^2
= 2 * 3.14 * 20.25
= 127.05 square inches
2. Area of the rectangle (the lateral surface area of the cylinder): 2 * π * radius * height
= 2 * 3.14 * 4.5 * 10.2
= 2 * 3.14 * 45.9
= 288.61 square inches
Now, add these two areas together to get the total surface area:
127.05 + 288.61 = 415.66 square inches
Therefore, Simone will need 415.66 square inches of patterned paper to cover the entire box. The closest option on the 7th grade formula sheet is 415.42 square inches.