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narnia85
22.12.2019 •
Mathematics
Leave answer in exact form unless otherwise indicated.
find the area of a segment formed by a chord 8" long in a circle with radius of 8".
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Ответ:
Area segment = 32/3 π - 16√3 inches²
Step-by-step explanation:
∵ The length of the chord is 8"
∵ The length of the radius of the circle is 8"
∴ the central angle of the segment is π/3 (60° the chord and the radii
formed an equilateral triangle)
∵ The area of the segment = area the sector - area Δ
∵ Area sector = 1/2 r²Ф
∵ r = 8" and Ф = π/3
∴ Area sector = 1/2 (8²) (π/3) = 32/3 π inches²
∵ Area Δ = 1/4 s²√3
∵ The length of the side is 8"
∴ Area Δ = 1/4 (8²) √3 = 16√3 inches²
∴ Area segment = 32/3 π - 16√3 inches²
Ответ:
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Step-by-step explanation: