solid mensuration
posted by Cathy .
Determine the area of the segment of a circle if the length of the chord is 15 inches & located 5 inches from the center of the circle.

Make your sketch
let the radius be r
r^2 = 5^2 + 7.5^2 = 81.25
r  √81.25
central angle formed by the chord:
let Ø be the angle at the centre formed by the rightangled triangle
tanØ = 5/7.5
Ø = 33.69°
central angle is 2Ø = 67.38°
area of whole circle = π(√81.25)^2 = 81.25π
so by simple ratio:
area of sector:
sector/84=1.25π = 67.38/360
sector = ....
area of triangle formed by the chord in that sector
= (1/2)(15)(5) = 75/2
area of segment = 75/2  area of sector
I will leave the button pushing up to you 
42.35

89
Respond to this Question
Similar Questions

Geometry
How would you solve these? The radius of a circle is 34 meters long, and a chord of the circle is 60 meters long. How far is the chord from the center of the circle? 
geometry
Two chords intersect a circle. The shorter chord is divided into segments of lengths of 9 inches and 12 inches. The longer chord has a length of 24 inches. Find the length of the shorter portion of the longer chord . 
geometry
If a chord 10 inches long is 5 inches from the center of a circle, find the radius of the circle. 
Maths
AB is a chord with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find d area of minor segment. A chord PQ of length 12cm suntends an angle of 120 degree at the centre of a circle. Find the … 
geometry
A diameter of a circle is perpendicular to a chord whose length is 12 inches. If the length of the shorter segment of the diameter is 4 inches, what is the length of the longer segment of the diameter? 
geometry
A diameter of a circle is perpendicular to a chord whose length is 12 inches. If the length of the shorter segment of the diameter is 4 inches, what is the length of the longer segment of the diameter? 
Geometry
In circle O, chord AB is 9 inches from the center. The diameter of the circle exceeds the length of AB by 2 inches. Find the length of AB 
Solid Mensuration
A circle having an area of 452 square inches is cut into two segments by a chord, which is 6 inches from the center of the circle. Find the area of the bigger segment. 
Solid mensuration
The area of a segment of a circle is 330 square meter. If the longest chord of the segment is 57 meter,find its radius. 
solid mensuration
a circle having an area of 452 square inches is cut into segments by a chord, which is 6cm from the center of the circle. Find the area of the bigger segment.