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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: /0 on July 26, 2008, 12:17:43 pm

Title: Cylindrical Container
Post by: /0 on July 26, 2008, 12:17:43 pm

A person stands on level ground 60 m from the nearest point of a cylindrical tank of radius length 20m. Calculate
(a) The circumference of the tank
(b) The percentage of the circumference that is visible to the person


I got (a), but I don't know how to get (b). Also, don't you require the height of the tank as well? The answers to (a) and (b) are 125.66 m and 41.96%. Thanks

Title: Re: Cylindrical Container
Post by: cara.mel on July 26, 2008, 12:27:01 pm

I have no idea what they are asking. It depends on where you are standing as to where the nearest point is

Eg if it looked like, with ratio size

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  ---------------------------------------------------------------------------------------------------------------
/    \                                                                                                           \
|    |                                                                                                           |
\   /                                                                                                            /
  ---------------------------------------------------------------------------------------------------------------
                                              . <- person 60m away
I doubt they would see very much circumference at all :P

Title: Re: Cylindrical Container
Post by: /0 on July 26, 2008, 12:33:43 pm

yeah true... ???

Title: Re: Cylindrical Container
Post by: ell on July 26, 2008, 01:29:53 pm

This is what it's asking:
(http://dl.getdropbox.com/u/57727/gmacyl.gif)

Hopefully you can figure it out from there :)

Title: Re: Cylindrical Container
Post by: cara.mel on July 26, 2008, 01:38:44 pm

How could you work out the tank was oriented that way etc from the question, I'm jealous

Title: Re: Cylindrical Container
Post by: ell on July 26, 2008, 01:52:46 pm

I remember doing this question last year, the chapter was about arc & chord lengths, circle theorems etc. so I just tried to draw a diagram that would use that knowledge, heh  ::)

Title: Re: Cylindrical Container
Post by: kaanonball on November 02, 2008, 01:26:46 am

a) Circumference = 2Pi * r = 2*3.14 * 20 = 125.66m

b) Sorry if my calculations are vague because to understand this question full you have to draw a proper diagram, so ill try to leave as many notes and details as i can

in order to find the amount of circumference visible we have to find arc length

first we have to find the angle of the minor sector

which is given by 180 - (90 + sin^-1 (20/80)) = 75.5225 * 2 = 151.045 degrees

NOTE: i multiplied by 2 because the 75.5225 is only the angle of half the minor sector
NOTE: i got 80m, as mans distance + radius gives the mans distance from the center of the tank
NOTE: the mans eyes make a 90 degree angle with the tank, hence why the angle is able to be determined using sine

now convert it to radians, 151.045 * pi/180 = 2.64 Radians

now find arc length, l =  20 * 2.64 = 52.7246

Divide arc length by circumference = 52.7246/125.66 = 0.41958

therefor the circumference visible to the man is 41.96% (i.e. 0.41958 * 100)

i hope that helps

Title: Re: Cylindrical Container
Post by: /0 on November 02, 2008, 01:37:27 am

lol thanks kaanonball...