circles geometry 17,18?

Question

17.what is the approximate area of a segment of a circle with a height 6m and the length of the chord is 20m? round your answer to the nearest whole number
a)8.54m2
b)73.6m2
c)85.4m2
d)746.67m2

18. what is the area of an ellipse with the major axis 20m and the minor 10m? round your answer to the nearest whole unmber
a)50m2
b)157m2
c)200m2
c)314m2

Answer 1

Problem 17.

The algorithm to be used is:

r = (c^2+4h^2)/(8h),
theta = 2 arcsin(c/[2r]),
s = r*theta,
d = r - h,
K = r^2[theta-sin(theta)]/2.

Where…

s = length of the arc
c = length of the chord
r = radius of the circle
h = height (the distance from the midpoint of the chord to the midpoint of the arc)
theta = the measure in radians of the central angle subtending the arc (where 0 ≤ theta ≤ pi).
d = apothem (the distance from the midpoint of the chord to the center of the circle)
K = the area of the segment of the circle

Then...

r = {(20^2)+[4*(6^2)]}/(8*6) = 11.3333 m

Theta = 2 arcsin(20/[2*11.3333]) = 2.1617 radians

s = 11.3333*2.1617 = 24.499 m

d = 11.3333-6 = 5.3333 m

and finally…

K = (11.3333^2)[2.1617-sin(2.1617)]/2 = 85.4961 sq. m

So the answer should be “c”

Rounded to the nearest whole number, area = 85 sq. m

Problem 18.

Area = Pi * A * B

Where

A = length of semi-major axis
B = length of semi-minor axis

Then…

Area = Pi * (20/2) * (10/2) = 157.0796 sq. m

So the answer should be “b”

Rounded to the nearest whole number, area = 157 sq. m

Answer 2

sorry , not sure