# solid mensuration

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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.

• solid mensuration -

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 right-angled 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

• solid mensuration -

42.35

• solid mensuration -

89

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