# Find the radius of the pulley if a rotation of 51.6 degrees raises the weight 11.4 cm

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The length of the arc measuring 51.6 degrees is 11.4 cm.

Use proportions to convert 51.6 degrees to radians:

`51.6/180=x/pi`

where x is the value of 51.6 degrees in radians. Solve for x:

`x=((51.6)(pi))/180=0.9` radians

The arc length is equal to the angle in radians multiplied by the radius of the circle:

Arc length=`=thetar`

Solve for r and substitute 11.4 cm for arc length and 0.9 for theta.

r=11.4/0.9=12.67

**Therefore the radius of the pulley is equal to 12.7 cm.**

Unitary method to find circumference of pulley

51.6 degree gives a lift of 11.4 cm

so 1degree gives a lift of (11.4/51.6) cm

so 360 degree gives a lift of (11.4/51.6)*360 =circumfrence of pulley

**Formula for circumfrence of circle is C = 2πr**

therefore (11.4/51.6)*360 = 2 *3.14 *radius of pulley

radius of pulley = (11.4*360)/(51.6*2*3.14) cm = 12.66 cm

**Ans- The radius of pulley is 12.66 cm :)**