Question

you graph a rectangle on a coordinate plane that has vertices (0,0), (3,0), (0,2), and (3,2). You then rotate that figure 360 degrees around the x axis creating a cylinder. Whats the surface area of a cylinder?

Explain the steps on how to figure it out

Answer 1

From the points given we know that the rectangle is 3 points wide and 2 points tall. If we rotate it $360^{\circ}$ around the x axis then we will receive the lying cyllinder which will be 3 points tall and 2 points wide (so its radius is 2/2 = 1 point). Now we can find the surface area of the cyllinder using appropriate formula:
$A=2\pi r^2 + 2\pi rh=2\pi*1^2 + 2 \pi * 1 * 3=2\pi + 6\pi=8\pi\approx 25.13$