Question

A circular pond is of diameter 100 m. It is surrounded by a 3 m wide path. Find the cost of painting the path at the rate of Rs. 20 per square metre (Use π = 3.14).​

Answer 1

Answer :-

• Total cost of painting the path = 19405.2 Rs

Given :-

• Width of Path = 3 m
• Diameter of Pond = 100 m

To Find :-

• Total cost of painting the path = ?

Explanation :-

In order to find the Cost of painting the path, first we need to find the area of circular path.

Finding Radius

$\rm \odot \: Radius \: of \: Pond \: (r) = \dfrac{100}{2} = \bold{50 \: m}$

$\rm \odot \: Radius \: of \: Pond \: With \: Path \: (R) = 50 + 3 = \bold{53 \: m}$

Finding Area of Path

$\purple { \boxed { \bf \bigstar \: Area \: of \: Path = Area \: of \: Path \: with \: Pond - Area \: of \: Pond \: \bigstar }}$

$\rm : \: \implies \pi \: (R^2 - r^2) \: m^2$

$\rm : \: \implies 3.14 \: [(53)^2 - (50)^2] \: m^2$

$\rm : \: \implies 3.14 \: (2809 - 2500) \: m^2$

$\rm : \: \implies 3.14 \times 309 \: m^2$

$\bf : \: \implies 970.26 \: m^2 \quad \star$

Finding the Cost of Painting,

$\rm \text{Cost of painting 1 m^2 } = 20 \: R_S$

$\rm \text{Cost of painting 970.26 m^2 }$

$\rm = (970.26) \times 20 \: R_S$

$\red { \underline { \boxed { \bf = 19405.2 \: R_S }}}$

Hence, the cost of painting the circular path is 19405.2 Rs.

Answer 2

Answer:

A circular pond is of diameter 100 m. It is surrounded by a 3 m wide path. Find the cost of painting the path at the rate of Rs. 20 per square metre (Use π = 3.14).