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The length of a rope, by which a cow is tied, is decreased from 22m

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New post 19 Aug 2015, 01:44
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The length of a rope, by which a cow is tied, is decreased from 22m to 14m. What is the decrease in the area that can be grazed by the cow?

(A) \(288\pi\)

(B) \(144\pi\)

(C) \(200\pi\)

(D) \(120\pi\)

(E) \(72\pi\)

Source : Aristotle Prep

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The length of a rope, by which a cow is tied, is decreased from 22m  [#permalink]

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New post 16 Feb 2016, 01:08
Length of the rope is the radius of the circle.

Decrease in the area grazed by the cow = \(\pi\) (\(22^2\) - \(14^2\))
= (22-14)(22+14)\(\pi\)
= 8(36)\(\pi\)
=288\(\pi\)

Answer: A
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The length of a rope, by which a cow is tied, is decreased from 22m  [#permalink]

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New post 18 Aug 2019, 05:53
One of the errors that GMAT exam makers want you to make here is confusing radius and diameter

Don't divide the 22m and 14m by two and use that resulting number as the radius because the whole length of the rope is already the radius!

1º Area (22m): 22^2 * pi = 484 * pi
2º Area (14m): 14^2 * pi = 196 * pi

Differences: 484 * pi - 196 * pi = 288 * pi

OPTION A
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Re: The length of a rope, by which a cow is tied, is decreased from 22m  [#permalink]

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New post 18 Aug 2019, 06:18
Gnpth wrote:
The length of a rope, by which a cow is tied, is decreased from 22m to 14m. What is the decrease in the area that can be grazed by the cow?

(A) \(288\pi\)

(B) \(144\pi\)

(C) \(200\pi\)

(D) \(120\pi\)

(E) \(72\pi\)

Source : Aristotle Prep


π(R^2 - r^2)

= π(R + r)(R - r)

= π (22+14)(22 - 14)

= π*36*8

= 288π, Answer must be (A)
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The length of a rope, by which a cow is tied, is decreased from 22m  [#permalink]

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New post 18 Aug 2019, 06:44
Gnpth wrote:
The length of a rope, by which a cow is tied, is decreased from 22m to 14m. What is the decrease in the area that can be grazed by the cow?

(A) \(288\pi\)

(B) \(144\pi\)

(C) \(200\pi\)

(D) \(120\pi\)

(E) \(72\pi\)

Source : Aristotle Prep


Given: The length of a rope, by which a cow is tied, is decreased from 22m to 14m.

Asked: What is the decrease in the area that can be grazed by the cow?

The decrease in the area that can be grazed by the cow \(= \pi 22^2 - \pi 14^2 = \pi (22^2 - 14^2) = \pi (22+14)(22-14) = \pi 36*8 = 288 \pi\)

IMO A
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The length of a rope, by which a cow is tied, is decreased from 22m   [#permalink] 18 Aug 2019, 06:44
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