A circular park is surrounded by a road 21, m | vedclass

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Question

Given that, a circular park is surrounded by a road.

Width of the road $=21\, m$

Radius of the park $\left(r_{i}ight)=105 \,m$

$	herefore$

Vedclass · Accepted Answer

$15246$

Vedclass · Answer

Given that, a circular park is surrounded by a road.

Width of the road $=21\, m$

Radius of the park $\left(r_{i}ight)=105 \,m$

$	herefore$ Radius of whole circular portion (park $+$ road).

$r_e=105+21=126\, m$

Now, area of road $=$ Area of whole circular portion $-$ Area of circular park

$=\pi r_{e}^{2}-\pi r_{i}^{2}$ $\left[	hereforeight.$ area of circle $\left.=\pi r^{2}ight]$

$=\pi\left(r_e^{2}-r_{i}^{2}ight)$

$=\pi\left\{\left(126^{2}-(105)^{2}ight\}ight.$

$=\frac{22}{7} 	imes(126+105)(126-105)$

$=\frac{22}{7} 	imes 231 	imes 21$ $\left[\because\left(a^{2}-b^{2}ight)=(a-b)(a+b)ight]$

$=66 	imes 231$

$=15246\, cm ^{2}$

Hence, the required area of the road is $15246\,cm ^{2}$.

A circular park is surrounded by a road $21\, m$ wide. If the radius of the park is $105\, m ,$ find the area of the road. (in $cm ^{2}$)

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