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Question

The circumference of a circle exceeds its diameter by 180 cm. Then  the circumference  is


A
180 cm
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B
300 cm
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C
175 cm
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D
264 cm
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Solution

The correct option is A $$264$$ cm
$$ Given-\\ The\quad circumference\quad of\quad a\quad circle\quad exceeds\quad its\quad diameter\quad by\quad 180cm.\\ To\quad find\quad out-\\ The\quad circumference\quad of\quad the\quad circle=C=?\\ Solution-\\ Let\quad r=radius\quad of\quad the\quad circle.\\ \therefore \quad Its\quad diameter=D=2r\quad and\\ its\quad circumference=C=2\pi r.\\ By\quad the\quad given\quad condition,\\ (C-D)cm=180cm\\ \Longrightarrow 2\pi r-2r=180\\ \Longrightarrow 2r(\pi -1)=180\\ \Longrightarrow 2r(\frac { 22 }{ 7 } -1)=180\\ \Longrightarrow r=\frac { 180\times 7 }{ 15\times 2 } cm=42cm.\\ \therefore \quad The\quad circumference=C=2\pi r=2\times \frac { 22 }{ 7 } \times 42cm=264cm.\\ Ans-\quad Option\quad D. $$

Mathematics

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