The surface area of a cylinder

Question

The radius of a cylindrical gift box is (22xplus+33) inches. The height of the gift box is twicetwice the radius. What is the surface area of the cylinder? Write your answer as a polynomial in standard form.
The surface area of the cylinder is

Answer 1

The surface area of a cylinder is the sum of the areas of the two circular surfaces and the rectangular curved surface in between.  The length of the rectangle is equal to the circumference of the circle.

 

Area of one circle = pi*radius^2 = pi * (22x + 33)^2 = pi * (484x^2 + 1452x + 1089).  Don't forget there are two circles.

Circumference of circle = length of rectangle = pi*diameter = 2*pi*radius = 2 pi * (22x+33) = pi * (44x + 66).

Height of rectangle = 2 * (22x+33) = (44x + 66).

Area of rectangle = (44x + 66) * pi * (44x + 66) = pi * (1936x^2 + 5808x + 4356)

Grand total = pi * (2904x^2 + 8712x + 6534)