An archived instance of a Calc III forum

Find and sketch the graph of a 3D object

mark

(10 pts)

For this problem, you’re going to find an equation describing a simple 3D object like a sphere or cylinder. You should then respond to this post by

Telling us your assigned 3D object,
Typing out your equation in LaTeX format, and
Including a 3D graph of your object.

You’re welcome to try any 3D graphing software that you know. I recommend that most folks try GeoGebra 3D, which has a simple, Desmos like interface for 3D graphs.

To get your assigned 3D object, choose your forum login name from the list below:

audrey

My assigned 3D object is the cylinder of radius 5 whose axis goes through the point (0,1,-4) and is parallel to the x-axis. Since the cylinder is parallel to the x-axis, the equation should be independent of x and depend on only y and z. Thus, the equation should be

(y-1)^{2}+(z+4)^{2}=25,

which produces the following 3D picture:

Here’s a link to the GeoGebra file that generated that image.

rstahles

My assigned 3D object is the cylinder of radius 1 whose axis goes through the point (3,0,-3) and is parallel to the x-axis. Since the cylinder is parallel to the x-axis, the equation should be independent of x and depend only on y and z. Thus, the equation should be:

(y+0)^2+(z+3)^2=1,

which produces the following 3D picture:

Here’s a link to the GeoGebra file that generated the image above.

Samwise

If the radius of your cylinder is 5, shouldn’t the equations equal 25 (because it should be the radius squared)?

Samwise

Did your assigned object tell you that it was parallel to the x-axis, or were you able to derive that from the center point?

rstahles

My assigned object told me that it was.

Colby_Howell

My assigned 3D object is the sphere of radius 4 centered at the point (-2,-2,-2). I think the equation for this sphere should be

(x+2)^2+(y+2)^2+(z+2)^2 = 16

Here is the graph of this object

nfitzen

My assigned object is the sphere of radius 4 centered at the point (-2,-4,0). Because, by definition, a sphere is the set of all points a fixed distance away from the center, the equation describing this object is as follows:

(x+2)^2+(y+4)^2+z^2=4^2

A graph is found below.

Samwise

My assigned object is a sphere with a radius of 6 centred at the point (2,1,3). The equation for this sphere would be

(x-2)^2 + (y-1)^2 + (z-3)^2 = 36

which gives us the following graph:

Samwise

Thank you! Wasn’t sure if I had missed something since mine didn’t specify.

sophiem

My assigned object is a sphere of radius 1 centered at the point (-2,-4,-2). The equation is:
(x+2)^{2}+(y+4)^2+(z+2)^2=1

Jake

My assigned 3D object is a sphere with a radius of 5, centered at point (-2,1,-4). My equation is:

(x+2)^{2}+(y-1)^{2}+(z+4)^{2}=25

Sara

My assigned 3D object was a sphere of radius 5 centered at the point (-1,0,-3). The equation I used was:

(x+1)^{2}+(y)^{2}+(z+3)^{2}=25

The resulting image is below.

mbanawan

My object is a cylinder with a radius of 5 whose axis goes through the point (3,-4,2) and is parallel to the x-axis. The equation should be:

(y+4)^2 + (z-2)^2 = 25

which gives the following 3D graph:

mhernan5

My assigned 3D object is a sphere or radius 3 centered at the point (2,2,-3). The equation for this sphere would be
(x-2)^2+(y-2)^2+(z+3)^2=9

scaldwe4

My object was a cylinder whose radius is 1 and goes through the point (-1,0,0) and is parallel to the x-axis.

(y-0)^2 + (z-0)^2 =1

mparog

My 3D object is a cylinder of a radius of 3 whose axis goes through the point (-1,2,3) and is parallel to the x-axis. The Formula is:

(y-2)^2 + (z-3)^2 = 9

The 3D picture is:

Alexander_The_OK

My equation to get a sphere with a radius of 3, centered at the point (2,3,3) is x^2-2x+y^2-3y+z^2-3z

vwinebar

My 3D object was a radius 1 cylinder parallel to the y-axis and center through (-4,3,3).

The equation I found was independent of Y, ((x+4)^2)+((z-3)^2)=1^2

myost

My assigned 3D object is the sphere of radius 5 centered at the point (1,-2,-3). The equation should be

(x-1)^2+(y+2)^2+(z+3)^2=25

Which produces the following 3D picture: