Question

352m परिधि वाले एक वृताकार पार्क के बाहर चारों ओर 7 मीटर चौड़ी एक सड़क है सड़क का क्षेत्रफल ज्ञात करें ​

Answer 1

Given:

352 m परिधि वाले एक वृताकार पार्क के बाहर चारों ओर 7 मीटर चौड़ी एक सड़क है|

To find:

सड़क का क्षेत्रफल ज्ञात करें ​|

Solution:

Finding the radius of the circular park:

The circumference of the park = 352 m

Also, Circumference of a circle = $2 \pi r$

∴ $2 \pi r = 352$

$\implies r = \frac{352 \times 7}{2 \times 22}$

$\implies \bold{r = 56 \:m}$

Finding the area of the road:

The width of the road outside the park = 7 m

So, the radius of the circular park along with the road = r + 7 = 56 + 7 = 63 m

Now,

The area of the road is,

= [Area of the circular park along with the road] - [Area of the circular park]

= [$\pi (r + 7)^2$] - [$\pi r^2$]

= [$\frac{22}{7} \times 63^2$] - [$\frac{22}{7} \times 56^2$]

= $\frac{22}{7} [63^2 - 56^2]$

= $\frac{22}{7} [3969 - 3136]$

= $\frac{22}{7} \times 833$

= $\bold{2618\:m^2}$

Thus, the area of the road is → 2618 m².

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