A circular garden with radius 42 m is surrounded from
outside by a path of 3.5 m wide. Find the cost to pave the
stones on the path at the rate of Rs. 20 per m2.
(Ans: Rs. 19250)
Answers
Answer:
Area of the circular garden = π r^2
Area of the circular garden = 22/7 × 42 × 42
= 5544 sq.m
Area of circular garden including
the path. = 22/7 × 45.5 × 45.5
= 6506.5 sq.m
Area of the path. = 6506.5 sq.m - 5544sq.m
Area of the path. = 962.5 sq.m
Rate of paving stones per m. = ₹20
Cost of paving the path. = ₹20 × 962.5
= ₹ 19,250.
Hope this helps you :)
Given :
→ Radius of a circular garden = 42 m
→ The circular garden is surrounded from outside by a path of width = 3.5 m
To find :
→ Cost to pave the stones on the path at the rate of Rs. 20 per m²
Concept :
Firstly, we will calculate the area of the path. To calculate the area of the path :-
Find the area of the circular garden using formula of area of circle. Add the width of path to the radius of the circular garden, the resultant value will be the radius of the circular garden including the path. The find the area of the circular garden including the path. To calculate the area of the path, subtract the area of cricular garden from the area of the circular garden including the path.To find the cost of paving the stones on the path, multiply the rate of paving by the area of the path. And we're done!!
Formula to calculate area of circle :-
Area of circle = πr²
where,
• Take π = 22/7
• r denotes the radius of the circle
Solution :
Area of the circular garden :
→ Area of circular garden = πr²
→ Substituting the given values :
→ Area of circular garden = 22/7 × (42)²
→ Area of circular garden = 22/7 × 42 × 42
→ Area of circular garden = 22 × 6 × 42
→ Area of circular garden = 5,544
Area of the circular garden = 5,544 m²
Radius of the circular garden including the path :
→ Radius of circular garden including the path = Radius of the circular garden + Width of the path
→ Radius = 42 + 3.5
→ Radius = 45.5
Radius of circular garden including the path = 45.5 m
Area of the circular garden including the path : → Area = πr²
→ Substituting the given values :
→ Area = 22/7 × (45.5)²
→ Area = 22/7 × 45.5 × 45.5
→ Area = 22 × 6.5 × 45.5
→ Area = 6,506.50
Area of circular garden including the path = 6,506.5 m²
Area of the path :
→ Area of the path = Area of the circular garden including the path - Area of the path→ Area of the path = 6,506.50 - 5,544
→ Area of the path = 962.50Area of the path = 962.5 m²
Cost of paving the stones on the path :
→ Cost of paving 1 m² of the path = Rs. 20
→ Cost of paving 962.5 m² of the path = 20 × 962.5 = 19,250
∴ Cost to pave the stones on the path at the rate of Rs. 20 per m² = Rs. 19,250