Question

The cost of turfing a uniform circular road around a circular garden at Rs 20 per sq metre is Rs21560 and the area of the garden is 1386 sq metre. Find the width of the circular road.

Give answer in a proper and disciplined way.......

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Answer 1

Given:

The cost of turfing a uniform circular road around a circular garden at Rs 20 per sq metre is Rs21560

The area of the garden is 1386 sq metre.

To find:

Find the width of the circular road.

Solution:

The total cost of turfing the uniform circular road around the circular garden = Rs. 21560

The cost of turfing per sq. meter of the circular road = Rs. 20

∴ The area of the uniform circular road around the garden is,

= $\frac{21560}{20}$

= 1078 m²

The area of the circular garden = 1386 m²

∴ The area of the circular garden along with the uniform circular road is,

= 1078 m² + 1386 m²

= 2464 m²

Let's assume,

"R" → represents the radius of the garden + road

"r" → represents the radius of the circular garden

∴ Area of garden + road = 2464

⇒ $\pi R^2 = 2464$

⇒ $\frac{22}{7} R^2 = 2464$

⇒ $R =\sqrt{ \frac{2464 \times 7}{22}}$

⇒ $R = \sqrt{784}$

⇒ R = 28 m

Also,

Area of garden = 1386

⇒ $\pi r^2 = 1386$

⇒ $\frac{22}{7} r^2 = 1386$

⇒ $r =\sqrt{ \frac{1386 \times 7}{22}}$

⇒ $r = \sqrt{441}$

⇒ r = 21 m

Now,

The width of the circular road is given by,

= [radius of the garden + road] - [radius of the garden]

= R - r

= 28 - 21

= 7 m

Thus, the width of the uniform circular road is → 7 m.

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Answer 2

Answer:

in up there is your answer

Step-by-step explanation:

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