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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Circles

Grade: 8-a Lesson: S1-L1

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per square meter (Use π = 3.14).
2	Step	Given	d = 17.5 m and wide = 2 m and rate = 25
3	Hint	\$ r = d/2\$	So \$r = 17.5/2\$ = 8.75
4	Tip	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	Hint	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\$ \$= 3.14 times (10.75 m)^2\$
9	Tip	Calculate the area of the inner circle (pond)
10	Step	Substituting the given values	Area of Inner Circle (Pond) = \$π times (Radius of Pond)^2\$ \$= 3.14 times (8.75 m)^2\$
11	Formula:	Calculate the area of the path	Area of Path = Area of Outer Circle - Area of Inner Circle
12	Step	Substituting the values	\$= 3.14 times (10.75 m)^2 - 3.14 times (8.75 m)^2\$
13	Step	After simplification	\$Area of path = 3.14 times 115.56 - 3.14 times 76.56\$
14	Step	After simplification	\$Area of path = 362.85 - 240.39\$
15	Step	After simplification	\$Area of path = 122.46\$
16	Formula:	Calculate the cost of constructing the path	\$Cost = Area of Path times Cost per m^2\$
17	Step	Substituting the values	\$Cost = 122.46 times 25\$
18	Step	After simplification	Rs 3061.5
19	Step	Therefore, the cost of constructing the path at the rate of Rs. 25 per square meter is Rs. 3061.5
20		Answer	C

Step

Type

Explanation

Answer

Problem

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

Step

Given

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

Hint

\$ r = d/2\$

So \$r = 17.5/2\$ = 8.75

Tip

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

Step

Substituting the given values

Outer radius = 8.75 + 2 = 10.75

Hint

Calculate the area of the outer circle

Formula:

The area of a circle is given by the formula

\$A = π times r^2\$

Step

Substituting the given values

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

Tip

Calculate the area of the inner circle (pond)

Step

Substituting the given values

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

Formula:

Calculate the area of the path

Area of Path = Area of Outer Circle - Area of Inner Circle

Step

Substituting the values

\$= 3.14 times (10.75 m)^2 - 3.14 times (8.75 m)^2\$

Step

After simplification

\$Area of path = 3.14 times 115.56 - 3.14 times 76.56\$

Step

After simplification

\$Area of path = 362.85 - 240.39\$

Step

After simplification

\$Area of path = 122.46\$

Formula:

Calculate the cost of constructing the path

\$Cost = Area of Path times Cost per m^2\$

Step

Substituting the values

\$Cost = 122.46 times 25\$

Step

After simplification

Rs 3061.5

Step

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

Answer