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# What is the area of the shaded region? (1) The difference in radius

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Math Expert
Joined: 02 Sep 2009
Posts: 55659

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11 Sep 2018, 03:09
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Difficulty:

55% (hard)

Question Stats:

50% (00:45) correct 50% (00:57) wrong based on 13 sessions

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What is the area of the shaded region?

(1) The difference in radius between the inner circle and the outer circle is 5.
(2) Angle x is 45°.

Attachment:

image003.jpg [ 4.71 KiB | Viewed 304 times ]

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11 Sep 2018, 04:23
Bunuel wrote:

What is the area of the shaded region?

(1) The difference in radius between the inner circle and the outer circle is 5.
(2) Angle x is 45°.

Attachment:
image003.jpg

Question: WHat is the area of shaded region?

Shaded area = $$(angle/360)*π(r_1^2 - r_2^2)$$
i.e. We need the angle drawn at the centre by these sectors and $$(r_1^2 - r_2^2)$$

Statement 1: The difference in radius between the inner circle and the outer circle is 5

$$(r_1^2 - r_2^2) = (r_1-r_2)*(r_1+r_2)$$

We only have the difference of the redie but not the sum and neither do we have the angle x drawn at the centre by the sectors hence

NOT SUFFICIENT

Statement 2: Angle x is 45°

we have the angle x drawn at the centre by the sectors but We do NOT have $$(r_1^2 - r_2^2) = (r_1-r_2)*(r_1+r_2)$$ hence

NOT SUFFICIENT

After combining the two statements

We only have the difference of the redie and also the angle drawn by sectors at the centre of the circle but we do NOT have the sum of the radie hence

NOT SUFFICIENT

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What is the area of the shaded region? (1) The difference in radius   [#permalink] 11 Sep 2018, 04:23
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