A circular wire is cut from a circle of radius 7.5 cm and wounded over a circumference of circular wheel of radius 120 cm.Find the angle made at centre of wheel by the wire.
Answer is π/8
write the step by step deviation
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Step-by-step explanation:
Here,
Circumference of the circle = 2πr
=2π ×7.5 cm = 15π cm
Now, circumference of the wheel= 2πr
= 2π×120cm
= 240π cm
The circumference of the wheel is at 360° as it is the complete circle whereas the new wire radius has changed and its circumference will not totally cover the wheel,
So here, Let x be the total angle of the smaller C.
240πcm = 360°
15π cm = x°
By cross multiplication we get
240πcm× x = 360×15πcm
x = 5400/240 = 22.5°
And your ans= π/8 = 180/8= 22.5
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