Question

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​

Answer 1

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