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The perimeter ( in metres) of a semicircle is numerically equal to its area (in square metres). The length of its diameter is (Take $\pi$ = $\frac{22}{7}$)1). $3\frac{6}{11}$ metres2). $5\frac{6}{11}$ meters3). $6\frac{6}{11}$ meters4). $6\frac{2}{11}$ meters |
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Answer» Given: The perimeter (in metres) of a SEMICIRCLE is NUMERICALLY equal to its area (in square meters). Formula Used: perimeter of a semicircle $\large = \pir + 2r Area of a semicircle = $ \large \FRAC{1}{2} π r^2$ Calculation: Let radius of semi CIRCLE = metres According to ques, Perimeter = Area ⇒ πr + 2r = $ \large \frac{1}{2} π r^2$ ⇒ π + 2 = $ \large \frac{1}{2} π r$ ⇒ r = $ \large \frac{2\pi + 4}{\pi}$ ⇒ r = 2 + 4 × $ \large \frac{7}{22}$ ⇒ r = 2 + $ \large \frac{14}{11} = \frac{36}{11}$ Diameter = 2 × $ \large \frac{36}{11} = 6\frac{6}{11} $ meters ∴ The diameter is $ \large 6\frac{6}{11} $ m |
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