# Volumes of Revolution

#### April 13, 2016

3D printed volumes.

It can be tricky explaining what you mean when you say to take a function and rotate it about the x-axis to create a volume. So, I made an OpenScad program to make 3d prints of functions, including having it subtract one function from another. I also 3d printed a set of axes to mount the volumes on (and a set of cross-sections of the volumes being rotated.

The picture above are the functions Mrs. C. gave her calculus class on a recent worksheet. Specifically:

$y = e^{-x}+2$

from which is subtracted:

$y = 0.5 x$

Citing this post: Urbano, L., 2016. Volumes of Revolution, Retrieved March 27th, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

# Finding Volumes Using the Disk Method

#### February 25, 2014

Student’s program to calculate the volume of a curve rotated around the x-axis using the Disk Method in Calculus.

This VPython program was written by a student, Mr. Alex Shine, to demonstrate how to find the volume of a curve that’s rotated around the x-axis using the disk method in Calculus II.

The program finds volume for the curve:

$y = -\frac{x^2}{4} + 4$

between x = 0 and x = 3.

To change the curve, change the function R(x), and to set the upper and lower bounds change a and b respectively.

volume_disk_method.py by Alex Shine.

from visual import*

def R(x):
y = -(1.0/4.0)*x**2 + 4
return y

dx = 0.5

a = 0.0

b = 3.0

x_axis = curve(pos=[(-10,0,0),(10,0,0)])

y_axis = curve(pos=[(0,-10,0),(0,10,0)])

z_axis = curve(pos=[(0,0,-10),(0,0,10)])

line = curve(x=arange(0,3,.1))
line.color=color.cyan
line.y = -(1.0/4.0) * (line.x**2) + 4

#scene.background = color.white

for i in range(-10, 11):

curve(pos=[(-0.5,i),(0.5,i)])
curve(pos=[(i,-0.5),(i,0.5)])

VT = 0

for x in arange(a + dx,b + dx,dx):

V = pi * R(x)**2 * dx

disk = cylinder(pos=(x,0,0),radius=R(x),axis=(-dx,0,0), color = color.yellow)

VT = V + VT

print V

print "Volume =", VT



Citing this post: Urbano, L., 2014. Finding Volumes Using the Disk Method, Retrieved March 27th, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.