Question

4. The length of the short circuit of a circle with a radius of 21 cm is 33 cm. Find the size of the angle at least in front of the center. Find the area of ​​the semicircle and the segment formed by this arc.​

Answer 1

Given : The length of the Sector cut   of a circle with a radius of 21 cm is 33 cm.

To Find :   size of the angle at  the center.

Area of sector cut off

Solution:

The length of the Sector cut   of a circle with a radius of 21 cm is 33 cm.

arc length = ( angle / 360° )2πR

=> 33 = (( angle / 360° )2(22/7)21

=> 33 = (( angle / 360° )2(22 )3

=> 33 = (( angle / 360° )2 * 66

=>1  = (( angle / 360° )2 * 2

=> 1  = (( angle /90° )

=>  angle  = 90°

area of  sector  = (90/360) πR²

= (1/4) (22/7) 21²

= 346.5 cm²

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