Question

Find the radius of a circle whose area is twice the area of a circle of radius 14 cm.
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Answer 1

Explanation:

$\mathbf\red{Given:-}$

• Radius of a circle = 14 cm

$\mathbf\blue{To\: Find}$

• The radius of a circle whose area is twice the area of a circle of radius 14 cm.

$\mathbf\green{Solution}$

$\tt\orange{Radius\: of\: circle = 14cm}$

$\tt\purple{Area\: of \:the \:circle = \pi{r}^{2}}$

$\tt\purple{\frac{22}{7} \times 14 \times 14}$

$\tt\purple{22 \times 2 \times 14}$

$\tt\purple{\implies 616{cm}^{2}}$

$\tt\orange{Area\: of \: circle\: with\: 14cm\: radius= 616{cm}^{2}}$

__________________

$\tt\pink{Twice\: the \: area \: of\: cirlce\: with\: 14cm\:radius}$

$\tt\pink{2\times 616}$

$\tt\pink{\implies 1232}$

$\tt\red{Radius\:of\:the\: circle =\sqrt{ \frac{area}{\pi} } }$

$\tt\red{ = \sqrt{ \frac{1232}{ \frac{22}{7} } } = \sqrt{ 1232 \times \frac{7}{22} }}$

$\tt\red{=\sqrt{392} = 19.7989}$

$\tt\pink{Therefore,\: the radius\:of\:cirlce\:whose\: area \:is \:twice\: the\: area \:of\: a \:circle \:of\: radius\: 14 cm\: is}$

$\huge\boxed{19.7989}$