the outer edge of a circular track is 440 m long.if is widened by 5m all around,find the cost of widening it at rate of 8 rs per m square?

18212 answer

To find the cost of widening the circular track, we need to calculate the area of the widened track first.

Given that the outer edge of the circular track is 440 m long, we can find the radius of the original track using the formula for the circumference of a circle:

Circumference = 2 * π * radius

440 = 2 * 3.14 * radius

Dividing both sides by 2 * 3.14, we get:

radius = 440 / (2 * 3.14)

radius ≈ 70.06 m

The radius of the original track is approximately 70.06 m.

To find the radius of the widened track, we add 5 m to both the length and width of the original track:

New radius = radius + 5

New radius ≈ 70.06 + 5 ≈ 75.06 m

The radius of the widened track is approximately 75.06 m.

The area of the original circular track can be calculated using the formula:

Area = π * (radius^2)

Area = 3.14 * (70.06^2)

Area ≈ 3.14 * 4913.6036 ≈ 15,412.45 m^2

The area of the widened circular track can be calculated using the same formula:

Area (widened) = π * (new radius^2)

Area (widened) = 3.14 * (75.06^2)

Area (widened) ≈ 3.14 * 5643.6036 ≈ 17,758.45 m^2

Now, to find the area of the widened track, we subtract the area of the original track from the area of the widened track:

Extra area = Area (widened) - Area

Extra area = 17,758.45 - 15,412.45

Extra area ≈ 2346 m^2

The extra area of the track that needs to be widened is approximately 2346 m^2.

To find the cost, we multiply the extra area by the rate:

Cost = Extra area * Rate

Cost = 2346 * 8

Cost = 18,768 rs

Therefore, the cost of widening the circular track at a rate of 8 rs per square meter is 18,768 rs.

To find the cost of widening the circular track, we need to first calculate the new circumference of the widened track. Then we can find the difference in the areas of the original and widened tracks. Finally, we can multiply the difference in area by the cost per square meter.

Step 1: Calculate the original circumference
The outer edge of the circular track is given as 440 m. Since the outer edge represents the circumference of a circle, we can use the formula: C = 2πr, where C is the circumference and r is the radius.

C = 440 m

To find the radius, we can rearrange the formula: r = C / (2π)

r = 440 m / (2π) ≈ 70.03 m

Step 2: Calculate the new circumference
The track is widened by 5 m on each side. Therefore, the diameter of the widened track will be increased by 10 m.

New diameter = 2r + 10 m

New radius = (2r + 10) / 2

Step 3: Calculate the new circumference using the new radius

New C = 2π * New radius

Step 4: Calculate the difference in the areas of the original and widened tracks

Original area = π * r^2
New area = π * (New radius)^2

Difference in area = New area - Original area

Step 5: Calculate the cost of widening

Cost = Difference in area * Rate per square meter (8 Rs/m^2)

Let's calculate each step:

Step 1: Calculate the original circumference
C = 2πr = 2π * 70.03 m ≈ 440 m

Step 2: Calculate the new circumference
New radius = (2r + 10) / 2 = (2 * 70.03 + 10) / 2 ≈ 75.03 m

New C = 2π * New radius = 2π * 75.03 ≈ 470.98 m

Step 3: Calculate the difference in the areas
Original area = π * r^2 = π * (70.03)^2 ≈ 15486.91 m^2
New area = π * (New radius)^2 = π * (75.03)^2 ≈ 17680.71 m^2

Difference in area = New area - Original area ≈ 17680.71 m^2 - 15486.91 m^2 ≈ 2193.80 m^2

Step 4: Calculate the cost of widening
Cost = Difference in area * Rate per square meter = 2193.80 m^2 * 8 Rs/m^2 = 17550.40 Rs

Therefore, the cost of widening the track at a rate of 8 Rs per square meter is approximately 17550.40 Rs.

2 pi Rin = 440

Rin = 70
Rout = 75

A = pi Rout^2 - pi Rin^2
= 2278 m^2

2278 * 8 = 18221