Solomon needs to justify the formula for the arc length of a sector. Which expression best completes this argument?The circumference of a circle is given by the formula , where d is the diameter.Because the diameter is twice the radius, .If equally sized central angles, each with a measure of , are drawn, the number of sectors that are formed will be equal to _____.The arc length of each sector is the circumference divided by the number of sectors, or .Therefore, the arc length of a sector of a circle with a central angle of is given by or .A.B.C.D.SUBMITarrow_backPREVIOUS
Question
Solomon needs to justify the formula for the arc length of a sector. Which expression best completes this argument?The circumference of a circle is given by the formula , where d is the diameter.Because the diameter is twice the radius, .If equally sized central angles, each with a measure of , are drawn, the number of sectors that are formed will be equal to _____.The arc length of each sector is the circumference divided by the number of sectors, or .Therefore, the arc length of a sector of a circle with a central angle of is given by or .A.B.C.D.SUBMITarrow_backPREVIOUS
Solution
It seems like there's a mistake in your question as it's incomplete and the options (A, B, C, D) are not provided. However, I can help you understand how to derive the formula for the arc length of a sector.
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The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle.
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Since the diameter is twice the radius, we can substitute d = 2r into the formula to get C = 2πr, where r is the radius of the circle.
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If we draw equally sized central angles each with a measure of θ (in degrees), the number of sectors that are formed will be equal to 360/θ.
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The arc length of each sector is the circumference divided by the number of sectors. So, the arc length (L) is given by L = C/(360/θ) = (2πr * θ)/360.
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Therefore, the arc length of a sector of a circle with a central angle of θ is given by L = (2πr * θ)/360 or L = (πr * θ)/180 if we simplify it.
Please provide the options so I can help you choose the correct one.
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