Circles Question Watch

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DOJO
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#1
Report Thread starter 14 years ago
#1
referring to the diagram, find :

a, the parimeter of the shaded region when the angle = 0.8 radians.
b, the value of the angle when the parimeter of the shaded region equals 14

any idea on how to do this question?

thanks!
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SsEe
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#2
Report 14 years ago
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Using arc length = rt (t=theta)
Perimeter = 2 + 2 + 3*0.8 + 5*0.8 = 10.4 cm
14 = 2 + 2 + 3t + 5t
solve to get t=5/4 radians
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DOJO
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#3
Report Thread starter 14 years ago
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(Original post by SsEe)
Using arc length = rt (t=theta)
Perimeter = 2 + 2 + 3*0.8 + 5*0.8 = 10.4 cm
14 = 2 + 2 + 3t + 5t
solve to get t=5/4 radians
I am really sorry but I do not understand how you did both steps.

L = r X theta, how did you relate tha to both questions:

for the first one I can see you have added up everything to get the parimeter like in a rectangle, however I do not understand why you added it twice to get 12 when 2+2+3+3 = 10 , so shouldnt it be l = 10*0.8?

The part I dont know how you used l=r * theta.

Sorry. Is it possible you could take me through all the steps slavishly, thanks!
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SsEe
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#4
Report 14 years ago
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The perimeter of the shaded bit is made up of two straight bits, each of length 2cm and two arcs. The smaller arc is from a sector of radius 3cm and angle 0.8 radians and the larger one is from a sector of radius 5cm and again, angle 0.8 radians. You just add all these up to get the total perimeter. So 2 + 2 + (using r*theta) 3*0.8 + 5*0.8 = 10.4cm

The second part works in the same way only the angle is the unknown. Perimeter is amde of 2 straight bits of length 2cm each. Then a small arc from a sector radius 3cm and angle t radians. And a larger arc from a sector of radius 5cm and angle t radians. You know that all these add up to 14. So 14 = 2 + 2 + 3t + 5t. Solve this to get t=5/4 radians.
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