Question

The inner and outer diameters of a circular path are 630 m and 658 m respectively.Find the area of the circular path.

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Find the area of the inner circle:

Diameter = 630 m

Radius = Diameter ÷ 2

Radius = 630 ÷ 2 = 315 m

Area = πr²

Area = π(315)²

Area = 99225π m²

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STEP 2: Find the area of the outer circle:

Diameter = 658 m

Radius = Diameter ÷ 2

Radius = 658 ÷ 2 = 329 m

Area = πr²

Area = π(329)²

Area = 108241π m²

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STEP 3: Find the area of the circular path:

Area = 108241π - 99225π

Area = 9016π m²

Area = 28336 m²

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Answer: Area of the circular path is 28,336 m²

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$\textbf {Cheers}$

Answer 2

Given,

Let the radius of inner circle be r and radius of outer circle be r+h where h width of circular path.

r = 630/2 = 315m

r +h = 658/2 = 329

h = 329 - 315 = 14m

$\text{Area of inner circle} = \pi r^{2} \\ \\ \text{Area of outer circle} = \pi (r+h)^{2} \\ \\ So, \\ \\ \text{Area of circular path = Area of outer circle - Area of inner circle} \\ \\ \ \ \ = \pi (r+h)^{2} - \pi r^{2} \\ \\ =\pi(r^{2} + h^{2} + 2hr - r^{2}) \\ \\ = \pi(h^{2} + 2hr) \\ \\ = \pi h(h + 2r) \\ \\ = \frac{22}{7}*14( 14 + 2*315) \\ \\ = 22*2(14 + 630) \\ \\ = 44* 644 \\ \\ = 28336 \ m^{2} \ \ \textbf{Ans.}$