Question

A circular park of radius 30 m has a road 5 m wide running around it. Find the cost of metalling the road at 12 rupee per sq m.​

Answer 1

Solution :

The radius of the circular park,

                                     r = 30 m

Now, the area of the circular park

   = πr² m²

   = π * 30² m²

   = 900π m²

Given that, the width of the road is 5 m

Now, the radius of the circular park along with the road around it

= (radius of the circular park) + (width of the road)

   = 30 + 5 m

         = 35 m

So, the area of the of the circular park along with the road around it

   = π (35)² m²

   = 1225π m²

Thus, the area of the road

= (the area of the circular park along with the road around it) - (the area of the circular park) m²

   = (1225π - 900π) m²

   = 325π m²

Thus, the cost of metalling the road at Rs 12 per m²

 = Rs (12 * 325π)

    = Rs (3900π)

       = Rs (3900 * 22 / 7)

          = Rs 12257.14

Answer 2

Given Radius of Circular Park=30 m

Area of Park=πr²

$= \pi \times 30 {}^{2} \\ \\ = \pi\times 30 \times 30 \\ = 900\pi$

Aprrox=900\pi

So Area of Park=900\pi

Now Road of Width 5m Running All Around It.

Now

Radius=Internal Circle Radius+Width of path.

Radius=30+5

Radius=35 m

Now Area.

πr²

$\pi \times {35}^{2} \\ \\ \pi \times 35 \times 35 \\ \\ = 1225\pi {m}^{2}$

Area of Path=$1225\pi-900\pi$

=$325\pi{m}^{2}$

Metalling per/m=₹12

Total Cost=$325\pi\times12$

=$325\times\frac{22}{7}\times12$
=₹12257.14

Approx=₹12257

$\boxed{\mathbf{Rs.12257}}$