1

Problem

A circular pond has a diameter of 17.5 m and is surrounded by a 2 m wide path. Calculate the cost of constructing the path at a rate of Rs. 25 per square meter (Use π = 3.14).

2

Step

Given value are

d = 17.5 m and wide = 2 m and rate = 25

3

Hint

the radius of the pond

4

Step

Calculate the outer radius of the path:

The outer radius is the sum of the radius of the pond and the width of the path

Outer Radius = Radius of Pond + Width of Path

5

Step

Substituting the given values:

Outer radius = 8.75 + 2 = 10.75

6

Step

Calculate the area of the outer circle.

7

Formula

The area of a circle is given by the formula: \$A = π \times r^2\$

8

Step

Substituting the given values:

\$Area of Outer Circle = π \times (Outer Radius)^2\$

\$Area of Outer Circle = 3.14 \times (10.75 m)^2\$ = 362.85

9

Formula

Calculate the area of the inner circle (pond).

10

Step

Plug the given values:

\$Area of Inner Circle (Pond) = π \times (Radius of Pond)^2\$

\$Area of Inner Circle (Pond) = 3.14 \times (8.75 m)^2\$ = 240.39

11

Formula

Calculate the area of the path: Area of Path = Area of Outer Circle - Area of Inner Circle.

12

Step

Plug the values into the formula:

Area of path = 362.85 - 240.39

Area of path = 122.46

13

Formula

Calculate the cost of constructing the pathway: \$Cost = Area of Path \times Cost per square meter\$.

14

Step

Substituting the values into the formula:

\$Cost = 122.46 \times 25\$

Cost = Rs.3061.5

15

Solution

Therefore, the cost of constructing the path at the rate of Rs. 25 per square meter is Rs. 3061.5.

16

Sumup

Please summarize steps

Choices

17

Choice-A

Although this option may seem close, it might arise from rounding or calculation errors

Wrong Rs. 3061

18

Choice-B

The result is inaccurate due to rounding errors or calculation mistakes

Wrong Rs. 3062.5

19

Choice-C

The answer is correct because it aligns with the calculated value

Correct Rs. 3061.5

20

Choice-D

The result is incorrect due to rounding errors or calculation mistakes

Wrong Rs. 3062

21

Answer

Option

C

22

Sumup

Please summarize choices