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Point O is the center of the circle. If the area of the circle is 36π

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Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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New post 21 Dec 2018, 01:39
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (00:37) correct 17% (00:42) wrong based on 29 sessions

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Point O is the center of the circle. If the area of the circle is 36π and the area of the rectangle is 72, what is the length of DC?

A. 4
B. 6
C. 8
D. 10
E. 12


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Capture (7).JPG [ 28.15 KiB | Viewed 256 times ]

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Re: Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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New post 21 Dec 2018, 02:21
area of circle = 36 pi

radius = 6

OD and OA = 6

rectanle we can say 6*x= 72
x= 12

so since OD= 6 ; DC = 12-6 = 6 IMO B



Bunuel wrote:
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Point O is the center of the circle. If the area of the circle is 36π and the area of the rectangle is 72, what is the length of DC?

A. 4
B. 6
C. 8
D. 10
E. 12


Attachment:
Capture (7).JPG

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Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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New post 21 Dec 2018, 04:49

Solution


Given:
    • O is the center of the circle
    • Area of the circle = 36ᴨ
    • Area of the rectangle = 72

To find:
    • The length of DC

Approach and Working:
Area of the circle = \(ᴨr^2 = 36 ᴨ\)
    • Thus, r = 6

Breadth of the rectangle = OA, which is the radius of the circle = 6
    • We know, l * b = 72
    • Thus, \(l = \frac{72}{6} = 12 = OC\)

OC = OD + DC = 6 + DC

Therefore, DC= 12 – 6 = 6

Hence, the correct answer is Option B

Answer: B

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Point O is the center of the circle. If the area of the circle is 36π &nbs [#permalink] 21 Dec 2018, 04:49
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