Perimeter of semicircle grassy plot = 72 m

Let r be the radius of the plot

Perimeter of semi-circle = 72 m

Width of path around it = 3.5 m

Perimeter of semi-circle = πr + 2r

= \( \dfrac{22}{7}+r+2r=72\)

= 22r + 14r = 72 × 7

= r = 14 cm

Radius including the width of path(R)

= r + 3.5 = 14 + 3.5 = 17.5 m

So,

area of path =\( \dfrac{\pi}{2}((17.5)^2-(14)^2)\)

= 173.25m^{2}

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).

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

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.