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 Problem, Clue, Hint, Formula, Steps and Solution

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