1.

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

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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