Question

A figure is located at (2, 0), (2, −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

Before anything do you have any answer choices?

Answer 2

No I don't have any.

Answer 3

Ah okay

Answer 4

Lets list the vertices (2, 0), (2, -2), (6, -2), and (6, 0)

A(2, 0)

B(2, -2)

C(6, -2)

D(6, 0)

Answer 5

The points with the same x-coordinate are on the same vertical line and the points having the same y-coordinates are on the same horizontal line.

Answer 6

okay

Answer 7

Alright so what do we have for line AB

Answer 8

For Line AB we have a vertical line segment

Answer 9

Line CD- A vertical line segment

line BC-A horizontal line segment

line AD- A horizontal line segment

Answer 10

Now we see that figure ABCD is has 2 pairs of parallel lines

One of which is vertical lines while the other is horizontal

Answer 11

The lines are perpendicular to each other, therefore giving us the interior angles of 90 degrees

Answer 12

Now we rotate figure ABCB

Answer 13

Hence gives us

y = Constant = The radius of the 3-D volume created by the rotation---> r

(a - b) = The length of the figure----> l

Plugging in 'r'(rotation), and 'y'(constant) in the above equation for v

Answer 14

Now the last step is easy to figure out