Question

solve with good explanation ☑☑​

Answer 1

Outer Diameter = 140 m.

⇒ Outer Radius = 140/2 = 70 m.

Perimeter of the Circle = 2πr

= 2 × 22/7 × 70

= 440 m.

∴ Cost of Fencing the Outer Part = 440 × Rs.7

= Rs.3080

Now,

Inner Radius = 70 + 7 = 77 m.

∴ Inner Perimeter = 2 × 22/7 × 77

= 44 × 11

= 484 m.

∴ Cost of Fencing the Inner Part = 484 × Rs. 7

= Rs. 3388

∴ Total cost of Fencing the the Inside and Outside of the Circle = 3080 +3388

= Rs. 6468.

Answer 2

Question

The diameter of the circular park is 140 m. around it on the outside a path having the width of 7 m is constructed. If the path has to be fenced from inside and outside at the rate of Rs. 7 per metre,find its total cost.

Given

• Diameter of the circular park = 140 m
• A path of width 7 m is constructed outside the circular park.
• Cost of fencing the 1 m² of the park = Rs. 7

To find

• Cost of fencing the circular park

Solution

Firstly, we will find the radius of the circular park by using the diameter.

Using formula,

Diameter = Radius/2

Substituting the values,

⟶ 140/2

⟶ 70 m

• Radius [inside] of the circular park = 70 m

We have to find the cost of fencing the circular park. So, for that we need the value of the boundary of the park. Boundary of the park means that we have to find the circumference of the park.

Using formula,

Circumference = 2πr

where,

• Take π = 22/7
• r = radius of the circular park

Substituting the given values,

⟶ 2 × 22/7 × 70

⟶ 44/7 × 70

⟶ 44 × 10

⟶ 440 m

• Circumference (inside) of the circular park = 440 m

Radius of the park (outside) = 70 + 7 = 77 m

Now, we will find the circumference of the circular park using the outer radius.

Using formula,

Circumference = 2πr

Substituting the given values,

⟶ 2 × 22/7 × 77

⟶ 44/7 × 77

⟶ 44 × 11

⟶ 484 cm

• Circumference of the circular park (outside) = 484 cm

Total circumference of the park = 440 + 484 = 924 cm

Cost of fencing the park = 924 × 7 = Rs. 6468

❖ Cost of fencing the park = Rs. 6468