A figure is located at (2, 0), (2, −2), (6, −2), and (6, 0) on a coordinate plane

Question

A figure is located at (2, 0), (2, −2), (6, −2), and (6, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.

Answer 1

The 2-dimensional figure is a 2 by 4 rectangle. Rotating it about the x-axis generates a right circular cylinder. The base has radius 2 and the length is 4.

Answer 2

First, plot the points in your X-Y plane. You will notice that they form a 2 by 4 rectangle. The second part is the tricky one: you have to imagine that you're looking at the X axis like if the tip of the axe was pointing to you, such that you can only see the small side of the rectangle. Once you do that, imagine rotating the rectangle 360 degrees around the X axis. The figure that results by rotating the rectangle in such a way is a cylinder. The base of the cylinder is a circle of base 2 (the small side of the original rectangle), and the height of the cylinder is 4 (the large side of the original rectangle). Hope this helps!

Answer 3

it's a cylinder, circular ends

height (on its side) = 6-2=4

circular bottom and top with area = 4pi

volume = 4pi(4) = 16pi cubic units

surface area = 24pi square units

it helps if you graph the 4 points. connecting them gives a rectangle

rotate it around the x axis and it's a cylinder, like a soup can only taller, and on its side