Question

A road which is 7m wide surrounds circular park whose circumference is 352m, Find the area of the road.

Answer 1

SOLUTION

Let the radius of the park be r m and its given that, circumference = 352m

=) 2πr= 352

=) 2×22/7×r= 352

=) r= 352× 7/44 = 56m

Therefore,

56m is the inner radius.

Now, outer radius = (56+ 7)m = 63m

=) Area of the road

=) [π(63)^2- π(56)^2

=) 22/7( 63+56) (63-56)

=) (22/7 × 119× 7)m^2

=) 2618m^2

hope it helps ✔️

Answer 2

Answer:

$\large 2618 \ m^2$

Step-by-step explanation:

Given :

Width of road = 7 m

Circumference = 352 m

We know that

Circumference of circle = 2 π r

Let radius be r m

2 π r = 352 m

π r = 176

r = 7 × 8 m

r = 56 m

It is radius of circular park.

So radius of circular park along road = 56 + 7 = 63 m

Area of the road = Area of  circular park along road - Area of circular park .

We know area of circle = $\pi r^{2}$

$\large \text{ Area of the road = \pi \ 63^{2} - \pi \ 56^{2} \ m^2 }\\\\\\\large \text{ Area of the road = \dfrac{22}{7}\times63\times63-\dfrac{22}{7}\times56\times56 }\\\\\\\large \text{ Area of the road = 22\times63\times9-22\times56\times8 }\\\\\\\large \text{ Area of the road = 12474-9856 }\\\\\\\large \text{ Area of the road = 2618 \ m^2 }$