I need some help with this...

Kantonar

New member
Joined
Apr 27, 2006
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1
ello everyone.

Ok, so I got this take home quiz for my math class (honors geometry -- I'm a freshman). This one problem ends up counting for more than 50% of the grade. Could someone help me out?

ok, here it is.

Two pulleys are connected by a belt.
The radii of the pulleys are 3cm and 15cm.
The distance between the two centers is 24cm.
Find the total length of the belt.

sorry for the poor quality pic, but I'm on a laptop and had to draw it in paint. Thanks in advance for your help...

math18im.png
 
Due to your excellent drawing, the straight pieces are easy.

24^2 = (Straight)^2 + (15-3)^2

Now what?
 
Hello, Kantonar!

As tkhunny said, it's an excellent diagram . . . Thank you!

Two pulleys are connected by a belt.
The radii of the pulleys are 3cm and 15cm.
The distance between the two centers is 24cm.
Find the total length of the belt.
Code:
              * * *
          *           *
        *               *
       *                 *
                                    * * *
      *         A         *       *       *
      *         *         * 24
      *         :         *     *     B     *
               C+ - - - - - - - * - - *     *
       *      15:        *      *     :     *
        *       :       *             :3
          *     :     *           *   :   *
              * * * - - - - - - - - * * *
                E                     D

Draw the line of centers AB=24\displaystyle AB\,=\,24

Draw a horizontal segment BC\displaystyle BC.

In right triangle ABC:AB=24,  AC=12\displaystyle ABC:\,AB\,=24,\;AC\,=\,12
    \displaystyle \;\;Hence: BC=123=DE\displaystyle \,BC\,=\,12\sqrt{3}\,=\,DE
    \displaystyle \;\; Moreover: ABC=30o\displaystyle \,\angle ABC\,=\,30^o

Extend AB\displaystyle AB to F\displaystyle F on circle B\displaystyle B
We find that: FBD=60o\displaystyle \angle FBD\,=\,60^o

Extend BA\displaystyle BA to G\displaystyle G on circle A\displaystyle A.
We find that: GAE=120o\displaystyle \angle GAE\,=\,120^o

And that is enough to determine the curved portions of the belt.
 
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