The centers of two belt pulleys, with radii of 3 cm and 6 cm, respectively, are 13 cm apart. Find the total area K enclosed by the belt.
4 answers
I really have no idea how to find the theta of the angles, help please
I assume you made a diagram
Because of the symmetry, let's just look at the top part of the diagram
Let the centre of the smaller circle be O and the centre of the larger circle be P
Let the point of contact of the belt to the smaller circle be A and to the larger circle B.
Draw a line parallel to AB from O to hit BP at C
You now have a rectangle AOCB and a right-angled triangle OPC with 90° at C
look at the right-angled triangle , you have OP = 13 and PC = 3
We can find angle OPC = Ø by
cosØ = 3/13
Ø = 76.658°
also by Pythagoras, OC = √160
thus AB=√160
We are now in a position to find the area of the rectangle and the area of the triangle.
Double that and you have the area of the stuff between the radii.
So all we need now is the area of the larger and smaller circle covered by the belts.
Would you agree with me that the angle covered by the belt in the larger circle is 206.685° ?
So now all you have to do is set up a ratio of
arclength1/(2π(6)) = 206.685/360
and for the smaller circle:
arclength2/(2π(3)) = 153.332/360
you do the arithmetic
Because of the symmetry, let's just look at the top part of the diagram
Let the centre of the smaller circle be O and the centre of the larger circle be P
Let the point of contact of the belt to the smaller circle be A and to the larger circle B.
Draw a line parallel to AB from O to hit BP at C
You now have a rectangle AOCB and a right-angled triangle OPC with 90° at C
look at the right-angled triangle , you have OP = 13 and PC = 3
We can find angle OPC = Ø by
cosØ = 3/13
Ø = 76.658°
also by Pythagoras, OC = √160
thus AB=√160
We are now in a position to find the area of the rectangle and the area of the triangle.
Double that and you have the area of the stuff between the radii.
So all we need now is the area of the larger and smaller circle covered by the belts.
Would you agree with me that the angle covered by the belt in the larger circle is 206.685° ?
So now all you have to do is set up a ratio of
arclength1/(2π(6)) = 206.685/360
and for the smaller circle:
arclength2/(2π(3)) = 153.332/360
you do the arithmetic
dihoihihihih
<p>This is Mathematics</p>
1 answer