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The inner edge of the outer lane of a circular racetrack with eight co

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The inner edge of the outer lane of a circular racetrack with eight co  [#permalink]

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14 Sep 2018, 01:07
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Difficulty:

55% (hard)

Question Stats:

50% (03:08) correct 50% (02:17) wrong based on 14 sessions

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The inner edge of the outer lane of a circular racetrack with eight concentric lanes is 210 feet from the center of the track and the outer edge is 212 feet from the center. If each lane is the same width then what is the area of the second lane from the center of the track?

A. $$796\pi$$

B. $$2,100\pi$$

C. $$8,400\pi$$

D. $$40,000\pi$$

E. $$48,400\pi$$

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Re: The inner edge of the outer lane of a circular racetrack with eight co  [#permalink]

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14 Sep 2018, 01:43
Bunuel wrote:
The inner edge of the outer lane of a circular racetrack with eight concentric lanes is 210 feet from the center of the track and the outer edge is 212 feet from the center. If each lane is the same width then what is the area of the second lane from the center of the track?

A. $$796\pi$$

B. $$2,100\pi$$

C. $$8,400\pi$$

D. $$40,000\pi$$

E. $$48,400\pi$$

radius of Ninth outermost circle - radius of Eigth outermost circle = 212-210 = 2
i.e. width of each track = 2

radius of Seventh outermost circle = 210-2 = 208
radius of Sixth outermost circle = 208-2 = 206
radius of Fifth outermost circle = 206-2 = 204
radius of Forth outermost circle = 204-2 = 202
radius of Third outermost circle = 202-2 = 200
radius of Second outermost circle = 200-2 = 198

Second track is made of second and third circle hence area of second track $$= π(200^2-198^2) = 796π$$

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Re: The inner edge of the outer lane of a circular racetrack with eight co  [#permalink]

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14 Sep 2018, 11:34
Bunuel wrote:
The inner edge of the outer lane of a circular racetrack with eight concentric lanes is 210 feet from the center of the track and the outer edge is 212 feet from the center. If each lane is the same width then what is the area of the second lane from the center of the track?

A. $$796\pi$$

B. $$2,100\pi$$

C. $$8,400\pi$$

D. $$40,000\pi$$

E. $$48,400\pi$$

if the give details are of the outermost lane then the inner most lane will be of 200-198 (feet)

The area of the lane will be like Pi*((200*200)-(198*198)).
=796Pi.=Option A
Re: The inner edge of the outer lane of a circular racetrack with eight co &nbs [#permalink] 14 Sep 2018, 11:34
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