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Tootsie Roll Pop

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by

Hope R

on 1 October 2013

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Transcript of Tootsie Roll Pop

Tootsie Roll Pop
Related Rates Project

Method
The method that I used to calculate the radius was by using measuring tape to identify the diameter, then dividing the value by 2.
Diameter= 4.5cm
Radius= 2.25cm
Collected Data
Time Radius (cm)
30 seconds 2.25cm
60 seconds 2.0cm
90 seconds 2.0cm
120 seconds 1.95cm
150 seconds 1.95cm
180 seconds 1.95cm
210 seconds 1.9cm
240 seconds 1.9cm
270 seconds 1.9cm
300 seconds 1.875cm
330 seconds 1.75cm
360 seconds 1.75cm
390 seconds 1.75cm
420 seconds 1.65cm
450 seconds 1.65cm
480 seconds 1.6cm
510 seconds 1.5cm



Y-axis= Radius (cm)
X-axis= Time (sec)
X-axis= Time (sec)
Linear Equation=
y=ax+b
y= -0.0012x + 2.154
Rate of Change=
change in y/ change in x
Average Rate of Change will be calculated using the first set of data with the last set of data.
First Set of Data= 2.25cm, 30sec
Last Set of Data= 1.5cm, 510 sec
Average Rate of Change= 2.25-1.5cm/ 30-510sec
0.75/(-480)=
-0.0015625 cm/sec
Y-axis= Volume (cm^3)
Rate of Change of Volume= change in y/ change in x
First set of data= ( 47.71cm^3, 30sec)
Last set of data= (14.14cm^3, 510sec)
Collected Data
Time (seconds)
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
510

Volume (cm^3)
47.71
33.51
33.51
31.06
31.06
31.06
28.73
28.73
28.73
27.61
22.45
22.45
22.45
18.82
18.82
17.16
14.14

Average Rate of Change=
47.71-14.14/ 30-510
= 33.57/(-480)
=0.0699375 cm^3/ second
Calculations for Average Value of the Rate of the Change of the Volume of the TRP
V= (4/3)pi(r^3)
d/dt(V= (4/3)pi(r^3))
dV/dt= (4pi/3) (3r xdr/dt)
dr/dt= -0.0015625 cm/sec
r= 1.5cm
dV/dt= 4pi/3 3(1.5) x (-0.0015625)
= 4pi/3 x 4.5 x (-0.0015625)
= (4.188790205) x 4.5 x (-0.0015625)
= (18.84955592) x (-0.0015625)
= -0.0294524311
Average Value of the Rate of the Change of the Volume of the TRP= -0.0294524311 or ~-0.0295 cm/sec
Full transcript