Question

A figure is located at (0, 0), (−3, −4), and (−3, 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

Plot the points

Answer 2

It's a triangle and we're rotating it around the x-axis

Answer 3

if you can't figure out what shape it'll form when you rotate, just take a piece of paper and cut out a triangle

and then spin it

what 3D shape does it form?

Answer 4

A triangular prism?

Answer 5

no

do you see how they rotate it? what shape is formed?

Answer 6

A cone

Answer 7

That's your answer!

Answer 8

Ok so it says "Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation."

Answer 9

I also have to include the dimensions of the cone

Answer 10

The explanation is just that you rotate it and it forms a cone

You could draw that image I sent so that way you could show how the shape is formed

Answer 11

But what are going to be the coordinates of the cone

Answer 12

As for the dimensions

Answer 13

so what is the radius of the cone?

and what is the height?

Answer 14

SA = π ⋅ r2 + πrs

Answer 15

No, that's the surface area formula for a CYLNDER

we're not trying to find the surface area

we just want to know the radius and height

just count

the height is from (0, 0) to (-3, 0)

what is that distance??

Answer 16

the radius is from (-3, 0) to (-3, -4)

so what is the distance?

Answer 17

The height is 6

Answer 18

no

how much does it take to go from 0 to -3

Answer 19

3

Answer 20

Exactly! So the height is 3

And now what about the radius

How much does it take to go from 0 to -4

Answer 21

4

Answer 22

Am i right?

Answer 23

You got it!

Answer 24

Is this a good explanation:
Well if the figure was to be rotated around the x-axis the 3-D shape would be a cone. So when you rotate the figure that the coordinates provided it forms a cone. Then for the dimensions the height of the cone is 3 and the radius of the cone is 4.

Answer 25

Sounds good