Question

The diameter of a circular park is 105m a 10.5m wide road run on the outside around it . Find the cost of constructing the road at ₹20 per m
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Answer 1

Given data :-

• The diameter of a circular park is 105m a 10.5m wide road run on the outside around it .
• The cost of constructing the road at ₹20 per square meter.

Solution :-

Let, circular park be A and outside road be B

Here,

→ Diameter of circular park = 105 m

So now,

→ Radius of circular park = ½ × Diameter

→ Radius of circular park = ½ × 105

→ Radius of circular park = 52.5 m

Now, we use formula to find area of circular park .

→ Area of A = πr²

→ Area of A = 22/7 × (52.5)²

→ Area of A = 22/7 × 2756.25

→ Area of A = 60637.5/7

→ Area of A= 8662.5 m² ......( 1 )

Now, we need to find area of circular park with 10.5 m wide road run on the outside around it.

→ Area of A with B = π ( r + 10.5 )²

→ Area of A with B = 22/7 (52.5 + 10.5)²

→ Area of A with B = 22/7 × ( 63 )²

→ Area of A with B = 22/7 × 3969

→ Area of A with B = 87318/7

→ Area of A with B = 12474 m² .....( 2 )

Now, subtract eq. ( 1 ) from eq. ( 2 )

→ Area of B = [Area of A with B] - [Area of A ]

→ Area of B = 12474 - 8662.5

→ Area of B = 3811.5 m²

The cost of constructing the road at ₹20 per square meter.

Hence,

→ Cost of constructing the road = 20 × 3811.5

→ Cost of constructing the road = ₹76230

Hence, the cost of constructing the road is ₹76230.