Question

A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of width of 0·7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq. m ?

Answer 1

Diameter of the circular park = 7 m
∴ Radius of the circular park, r =\[\frac{7}{2}\] = 3.5 m

Width of the path = 0.7 m
∴  Radius of the park including the path, R = 3.5 + 0.7 = 4.2 m
Area of the path

\[= \pi R^2 - \pi r^2 \]
\[ = \pi\left( R^2 - r^2 \right)\]

\[= \frac{22}{7}\left( 4 . 2^2 - 3 . 5^2 \right)\]
\[ = \frac{22}{7} \times \left( 4 . 2 - 3 . 5 \right) \times \left( 4 . 2 + 3 . 5 \right)\]
\[ = \frac{22}{7} \times 0 . 7 \times 7 . 7\]
\[ = 16 . 94 m^2\]

Rate of cementing the path = Rs 110/m²      (Given)
∴ Total cost of cementing the path
= 16.94 × 110
= Rs 1863.40
Thus, the expenditure of cementing the path is Rs 1863.40.