What is the radius of circle if it has a sector with area 55.85 cm? and an arc length 40π/9 cm?
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What is the radius of circle if it has a sector with area 55.85 cm? and an arc length 40π/9 cm?
Paki sagot naman po...
auto brainliest ang maka sagot
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Answer:
25.1325/π cm
Step-by-step explanation:
Step-by-step explanation:
\rm Area \ of \ sector = Area_{\huge \circ} (\frac{arc \ length}{circumference})Area of sector=Area
∘
(
circumference
arc length
)
Given:
\rm Area \ of \ sector = 55.85Area of sector=55.85
\rm Arc \ length = \frac{40\pi}{9}Arc length=
9
40π
Substitute the value of the area of sector and arc length.
\implies \rm 55.85 = Area_\circ (\frac{12}{circumference})⟹55.85=Area
∘
(
circumference
12
)
We know that \rm Area_\circ = \pi r^2Area
∘
=πr
2
and \rm Circumference = 2\pi rCircumference=2πr
Thus,
\implies \rm 55.85 = \pi r^2(\frac{\frac{40\pi}{9} }{2\pi r})⟹55.85=πr
2
(
2πr
9
40π
)
\implies \rm 55.85 = \pi r^2(\frac{40\pi}{9} \times \frac{1}{2\pi r} )⟹55.85=πr
2
(
9
40π
×
2πr
1
)
\implies \rm 55.85 = \pi r^2(\frac{20}{9r})⟹55.85=πr
2
(
9r
20
)
\implies \rm 55.85 = \frac{20\pi r}{9}⟹55.85=
9
20πr
\implies \rm 55.85(9) = 20\pi r⟹55.85(9)=20πr
\implies \rm 502.65 = 20\pi r⟹502.65=20πr
\implies \rm \frac{502.65}{20\pi} = r⟹
20π
502.65
=r
\implies \boxed{\rm \frac{25.1325}{\pi} = r}⟹
π
25.1325
=r
#CTO