Question

The circumference of circle exeds its diametre by 30 cm . Find the radius of circle​

Answer 1

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$\large{\sf{\underline{\underline\pink{Solution!!}}}}$

Let the diameter be x.

We know that,

$\large\boxed{\underline{\orange{\sf Radius = \dfrac{diameter}{2}  }}}$

So,

$\red\longrightarrow\:\: \sf{Radius=\dfrac{x}{2}}$

$\small{\sf{\underline{\underline\purple{According\:to\:the\:question:-}}}}$

$\green\longrightarrow\:\: \sf{Circumference\:of\:the\:circle=x+30}$

$\green\longrightarrow\:\: \sf{2\pi r=x+30}$

$\green\longrightarrow\:\: \sf{2\times \dfrac{22}{7} \times \dfrac{x}{2} =30}$

$\green\longrightarrow\:\: \sf{ \dfrac{22x}{7} =x+30}$

$\green\longrightarrow\:\: \sf{ 22x=7(x+30)}$

$\green\longrightarrow\:\: \sf{ 22x=7x+210}$

$\green\longrightarrow\:\: \sf{ 22x-7x-210=0}$

$\green\longrightarrow\:\: \sf{15x=210}$

$\green\longrightarrow\:\: \sf{x=\dfrac{210}{15} }$

$\green\longrightarrow\:\:\underline{\boxed{\pink{\sf{x = 14 }}}}$

$\displaystyle\therefore\:\underline{\textsf{Diameter = \textbf{ 14}}}$

$:\implies\:\: \sf{Radius = \dfrac{14}{2} }$

$:\implies\:\: \sf{Radius = 7 }$

$\displaystyle\therefore\:\underline{\textsf{Radius = \textbf{ 7}}}$

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