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The area of a circular sector is 1790 centimetres squared and the central angle is 1.5 radians.
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Find the radius of the circle, giving the answer to the nearest centimetre.
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So letβs see if we can represent this information on a diagram.
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We have a circular sector; its area is 1790 centimetres squared and the measure of its central angle is 1.5 radians.
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And we are required to find the radius of the circle, which Iβm going to call π.
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There is a formula for the area of a circular sector.
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The area is equal to half the radius squared times the measure of the central angle in radians.
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We are given the area of the circular sector; itβs 1790 centimetres squared, and we are also given the measure of the central angle in radians, 1.5.
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Substituting those into the equation we have, we have an equation in terms of π alone.
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Multiplying both sides by two, we get 3580 equals π squared times 1.5.
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Swapping both sides and dividing by 1.5, we get that π squared is equal to 2386.6 recurring.
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And taking square roots on both sides, we get that π is equal to 48.85 dot dot dot.
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And of course, as the area was given in centimetres squared, this radius length will be in centimetres.
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And the only thing left to do is to round this answer to the nearest centimetre.
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So we get that the radius of the circle is 49 centimetres long.