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    Subject

    Bank Exam

    Topic

    Modhumoti Bank Ltd. - Probationary Officer - 2016

    The side length of a square inscribed in a circle is 2. What is the area of the circle ?

    ক)
    \(2\pi \)
    খ)
    \(\pi \)
    গ)
    \(\pi \)r2
    ঘ)
    \(2\sqrt 2 \)

    Explanation

    Solution: অনুবাদঃ বৃত্তের ভিতরে বর্গের এক বাহুর দৈর্ঘ্য 2. বৃত্তের আয়তন কত ? এখানে, বৃত্তের পরিসীমা = 2 ×2=22\sqrt 2  \times 2 = 2\sqrt 2 বৃত্তের ব্যাসার্ধ = 222=2\frac{{2\sqrt 2 }}{2} = \sqrt 2 বৃত্তের ক্ষেত্রফল = π(2)2  =2π\pi {(\sqrt 2 )^{2\;}} = 2\pi Alternative:    পাশের চিত্র মতে, পীথাগোরাসের উপপাদ্য অনুসারে, AB 2 + AD 2 = BD 2 => 2 2 + 2 2 = BD => BD 2 = 8 BD = 222\sqrt 2 Area of circle = π  r2  =π(222  )2  =2π\pi \;{r^{2\;}} = \pi {(\frac{{2\sqrt 2 }}{2}\;)^{2\;}} = 2\pi

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