Question

A road which is $$7$$ m wide surrounds a circular park whose circumference is $$88 m$$. Find the area of the road.

Answer 1

Given

$$w=7m$$

$$2\pi r=88m$$

$$\Rightarrow 2.\dfrac{22}{7} r=88$$

$$\Rightarrow 2.\dfrac{1}{7}.r=4$$

$$\Rightarrow r=2\times 7$$

$$r=14$$

So, $$r=14$$

$$R=r+w=14+7=21$$

$$\therefore$$ Area of road $$=\pi R^2-\pi r^2$$

$$=\pi (R+r)(R-r)$$

$$=\dfrac{22}{7}(21+14)(21-14)$$

$$=\dfrac{22}{7}(35)(7)$$

$$=770m^2$$