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In the diagram above, the clock shows that it is five minutes after 9

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In the diagram above, the clock shows that it is five minutes after 9  [#permalink]

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New post 25 Feb 2019, 02:17
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In the diagram above, the clock shows that it is five minutes after 9 o’clock. If the radius of the clock is 9 inches, what is the area of the sector created by the hands of the clock starting at 9 and moving clockwise?

A. 6π
B. 13.5π
C. 27π
D. 81π
E. 54π

Attachment:
2019-02-25_1316.png
2019-02-25_1316.png [ 42.62 KiB | Viewed 365 times ]

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Re: In the diagram above, the clock shows that it is five minutes after 9  [#permalink]

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New post 25 Feb 2019, 02:47
Area of sector = (pi)r^2*C/360
C = 120 degrees (angle intended at center)
r = 9 inches (given)

Substituting values, Area = 27(pi)

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In the diagram above, the clock shows that it is five minutes after 9  [#permalink]

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New post Updated on: 25 Feb 2019, 08:35
Bunuel wrote:
Image
In the diagram above, the clock shows that it is five minutes after 9 o’clock. If the radius of the clock is 9 inches, what is the area of the sector created by the hands of the clock starting at 9 and moving clockwise?

A. 6π
B. 13.5π
C. 27π
D. 81π
E. 54π

Attachment:
2019-02-25_1316.png


angle made by clock
11/2 * min ; 11* 5/2 ; ~ 28 * 90 + 28 or say 117.5 * ; ~ 118 *
118/360 * pi * 9^2 ; ~ 27 pi
IMO C
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Originally posted by Archit3110 on 25 Feb 2019, 04:49.
Last edited by Archit3110 on 25 Feb 2019, 08:35, edited 2 times in total.
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Re: In the diagram above, the clock shows that it is five minutes after 9  [#permalink]

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New post 25 Feb 2019, 08:28
Bunuel wrote:
Image
In the diagram above, the clock shows that it is five minutes after 9 o’clock. If the radius of the clock is 9 inches, what is the area of the sector created by the hands of the clock starting at 9 and moving clockwise?

A. 6π
B. 13.5π
C. 27π
D. 81π
E. 54π

Attachment:
2019-02-25_1316.png


60 Min = 360°

So, 1 min = 6°

And , 5 Min = 30°

Thus, the angle represented by the minute and hour hand is 90° + 30° = 120°

Area of the sector is \(\frac{120}{360}*π*9^2 = 27π\), Answer must be (C) 27π
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Re: In the diagram above, the clock shows that it is five minutes after 9  [#permalink]

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New post 27 Feb 2019, 10:17
Bunuel wrote:
Image
In the diagram above, the clock shows that it is five minutes after 9 o’clock. If the radius of the clock is 9 inches, what is the area of the sector created by the hands of the clock starting at 9 and moving clockwise?

A. 6π
B. 13.5π
C. 27π
D. 81π
E. 54π

Attachment:
2019-02-25_1316.png


Since there are 12 numbers, each numerical interval on the clock represents 360/12 = 30 degrees. Thus, we see that the angle created is 120 degrees, which is 1/3 of the area of the circle.

Since the area of the circle is 81π, the area sector is 1/3 x 81 = 27π.

(Technically, the angle between 9 and 1 when the clock shows 9:05 is slightly less than 120 degrees because the hour hand has progressed 5/60, or 1/12 x 30 degrees = 2.5 degrees, when it is 9:05. Thus, the sector angle is actually 120 - 2.5 = 117.5 degrees. This translates to 117.5/360 = 0.326 of the circle. Since the circle has an area of 81π, the sector area is 81π x 0.326 = 26.4π. The closest answer is choice C.).

Answer: C
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Re: In the diagram above, the clock shows that it is five minutes after 9   [#permalink] 27 Feb 2019, 10:17
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