SOLUTION: A circle having an area of 201.062 cm2 is to be divided into two segments by a chord which is 3 cm from the center of the circle. a. Compute the area of the smaller segment.

Question 1169602: A circle having an area of 201.062 cm2
is to be divided into two segments by a chord which is 3 cm from the center
of the circle.
a. Compute the area of the smaller segment.
b. Determine the area of the larger segment.
3. A wheel has a diameter of 100 centimeters. The wheel is supporting a cart moving at 48 kilometers per hour. What
is the angular velocity of the wheel in rpm?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The area of the smaller "pie wedge" sector, A_sector = R^2*theta/2,
where R = the radius, theta = the wedge angle.
Since the chord is 3 cm from the center, the half angle is given by:
arccos(3/R) = 1.1864. Thus the angle theta = 2.373.
The area of the segment will be the sector area minus the triangular portion
The area of this portion is 2(3*sqrt(R^2-3^2)/2) = 3*sqrt(55)
The radius, R = sqrt(A/pi) = sqrt(201.062/pi) = 8
Finally, the area of the segment is 75.9296 - 3*sqrt(55) = 53.681

RELATED QUESTIONS
A circle having an area of 201 cm2 is cut into segments by a chord which is 3 cm from the (answered by Boreal)

a circle is divided into two parts by a chord, 3cm away from the center, find the area of (answered by Edwin McCravy)

Find the area of the larger segment whose chord is 8" long in a circle with an 8" (answered by Alan3354)

A chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circle. (answered by ankor@dixie-net.com)

1.) The area of a circle is 201 cm. Which is the circumference of the... (answered by RedemptiveMath)

how to find the radius of a circle if a 24 cm chord is 9 cm from the... (answered by Edwin McCravy)

A chord is 20 cm long and is 6 cm from the center.How long is the chord that is 4 cm from (answered by ankor@dixie-net.com)

The area of a triangle is divided into 3 equal parts by line segments parallel to one... (answered by ikleyn)

A circle has a diameter of 32 cm. How far from the center of the circle, to the nearest... (answered by josgarithmetic)