Derrick has a white cylindrical storage box that he would like to decorate with patterned paper. The radius of the box is 6.5 and the height is 10in The cylinder's net is shown below.

Question

How much paper will Derrick need to cover the entire box? Use .
Responses
A:673.53in
B:1,326.65
C:2,918.63
D:540.87

Answer 1

To calculate the surface area of the cylinder, we need to find the lateral surface area and the area of the two circular bases.

Lateral surface area = 2πrh
Lateral surface area = 2 * π * 6.5 * 10
Lateral surface area = 407.96 in²

Area of two circular bases = 2πr²
Area of two circular bases = 2 * π * 6.5²
Area of two circular bases = 265.48 in²

Total surface area = Lateral surface area + Area of two circular bases
Total surface area = 407.96 + 265.48
Total surface area = 673.44 in²

Therefore, Derrick will need 673.44 in² of patterned paper to cover the entire box.

So, the closest answer choice is A: 673.53 in².