Belt & pulley problem

Hi everybody, I require assistance in solving this problem:

A transmission belt passes tightly around 2 pulleys and crosses itself between them. The radii of the pulleys are 3m and 2m respectively, and their centres are 13m apart. Calculate:

a) the length of the belt
b) the total area enclosed by the belt.

Answers
a) 43.65m
b) 56.75m^2

I would like to know the working out required for these questions.

I have also attached a simple diagram of the problem to aid in visualisation. Any assistance would be much appreciated.

Quote:

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Originally Posted by Xyrios

Hi everybody, I require assistance in solving this problem:

A transmission belt passes tightly around 2 pulleys and crosses itself between them. The radii of the pulleys are 3m and 2m respectively, and their centres are 13m apart. Calculate:

a) the length of the belt
b) the total area enclosed by the belt.

Answers
a) 43.65m
b) 56.75m^2

I would like to know the working out required for these questions.

I have also attached a simple diagram of the problem to aid in visualisation. Any assistance would be much appreciated.

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I've attached a sketch of the construction of the 2 interior tangents of 2 circles.

Use the greyed right triangle to calculate the tangent segments and the central angles which you have to use to calculate the 2 arcs of the circles.