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# If x = 40 degrees, what is the area of the sector shown in the figure?

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Math Expert
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If x = 40 degrees, what is the area of the sector shown in the figure?  [#permalink]

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24 Aug 2018, 05:19
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Difficulty:

15% (low)

Question Stats:

88% (00:28) correct 12% (01:10) wrong based on 38 sessions

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If x = 40 degrees, what is the area of the sector shown in the figure?

(1) The radius of the circle is 5.
(2) The circumference of the circle is 10π.

Attachment:

image001.jpg [ 3.17 KiB | Viewed 566 times ]

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Re: If x = 40 degrees, what is the area of the sector shown in the figure?  [#permalink]

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24 Aug 2018, 05:26
From 1: Area os sector = πr^2*40/360.
1 is sufficient.

From 2: C=2πr. r = 5.
Again sufficient.

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Re: If x = 40 degrees, what is the area of the sector shown in the figure?  [#permalink]

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24 Aug 2018, 05:29
Bunuel wrote:

If x = 40 degrees, what is the area of the sector shown in the figure?

(1) The radius of the circle is 5.
(2) The circumference of the circle is 10π.

Attachment:
image001.jpg

Determining Area of sector:-
a) Radius and b)Angle of sector are the basic requirement.

St1:- The radius of the circle is 5.
Sector angle and radius is known.
Sufficient.

St2:- The circumference of the circle is 10π.
Radius can be calculated if circumference is given. Sector angle is already given.
Sufficient.

Ans. (D)
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Re: If x = 40 degrees, what is the area of the sector shown in the figure?  [#permalink]

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24 Aug 2018, 10:05

Solution

Given:
• x = 40 degrees

To find:
• Area of the sector shown in the figure

Approach and Working:
• Area of a sector which subtends an angle of x degrees at the center = ᴨr2 * x/360, where r is the radius of the circle
• We know x, we need the value of ‘r’ to find the answer

Analysing Statement 1
• We are given that r = 5
Therefore, Statement 1 alone is sufficient to answer this question

Analysing Statement 2
• We are given that 2ᴨr = 10ᴨ
• Implies, r = 5
Therefore, Statement 2 alone is sufficient to answer this question.

Hence, the correct answer is option D.

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Re: If x = 40 degrees, what is the area of the sector shown in the figure?   [#permalink] 24 Aug 2018, 10:05
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