The cost of turfing a uniform circular road around a circular garden a

1.	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.......
Answer» 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. --------------------------------------------------------------------------------------- Also View: The inside perimeter of a running track is 400m. The LENGTH of each of the straight portion is 90m and the ends are semi-circles. If the track is 14m wide everywhere, find the area of the track. Also, find the length of the outer running track. brainly.in/question/839595 A watered circular field (SHADED) is inscribed in a square plot of land. The square plot has sides of length 500 meters. What is the area of the land that is not watered? brainly.in/question/16199461

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.......

Answer»

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.

---------------------------------------------------------------------------------------

Also View:

The inside perimeter of a running track is 400m. The LENGTH of each of the straight portion is 90m and the ends are semi-circles. If the track is 14m wide everywhere, find the area of the track. Also, find the length of the outer running track.

brainly.in/question/839595

A watered circular field (SHADED) is inscribed in a square plot of land. The square plot has sides of length 500 meters. What is the area of the land that is not watered?

brainly.in/question/16199461