Question

A circular flower bed is surrounded by a path $$4$$m width. The diameter of the flower bed is $$66$$m. What is the area of this path?(Take $$\pi =3.14$$)

Answer 1

Diameter of the circular flower bed$$=66$$m

$$\therefore$$ Radius of circular flower bed$$(r)=\dfrac{66}{2}=33$$m

$$\therefore$$ Radius of circular flower bed with $$4$$ m wide path$$(R)=33+4=37$$m

According to the question,
Area of path$$=$$Area of bigger circle$$-$$Area of smaller circle
$$=\pi R^2-\pi r^2=\pi(R^2-r^2)$$

$$=\pi[(37)^2-(33)^2]$$

$$=3.14[(37+33)(37-33)]$$ $$[\because a^2-b^2=(a+b)(a-b)]$$

$$=3.14\times 70\times 4$$

$$=879.20m^2$$.

Therefore, the area of the path is $$879.20m^2$$.