If the area and arc length of the sector of the circle is 60 cm² and 20 cm respectively, then the diameter of the circle is
Approved Tutor Answer10 Months agoTo find the diameter of the circle given the area and arc length of the sector, we can use the following formulas:
The area (A) is 60 cm² and the arc length (L) is 20 cm. We need to find the radius (r) first.
From the arc length formula, we can express θ in terms of r:
20 = (θ/360) × 2πr
Rearranging gives:
θ = (20 × 360) / (2πr) = (7200) / (2πr) = (3600) / (πr)
Now, substitute θ into the area formula:
60 = (θ/360) × πr²
Substituting for θ:
60 = ((3600)/(πr) / 360) × πr²
60 = (10r)
Thus, r = 6 cm.
The diameter (d) is twice the radius:
d = 2r = 2 × 6 = 12 cm.
The diameter of the circle is 12 cm, which corresponds to option b).
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