Question

(i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path.

(ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.

Answer 1

(i)

Area of the path = Area of outer circle - area of the inner circle

R = 17+8 = 25 m

r = 17 m

Area of the path $=\pi R^2-\pi r^2=\pi (R^2-r^2)=\frac{22}{7}\times ({25}^2-{17}^2)=\frac{22}{7}\times (625-289)=\frac{22}{7}\times 336=1056m^2$

(ii) The diameter of the park is 7 m
the radius of the park is 3.5 m
the width of the park is 0.7 m

smaller radius of park is 3.5 m
and bigger radius of park is 0.7+3.4 = 4.2 m

area of path =area of the outer circle -an area of the inner circle

$=\frac{22}{7}\times ({4.2}^2-{3.5}^2)=\frac{22}{7}\times (17.64-12.25)=\frac{22}{7}\times \left(5.39\right)=22\times 0.77=16.94m^2\text{The expenditure of cementing the path}=\text{rate}\times \text{area}=110\times 16.94=Rs1864.40$