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Bunuel

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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Bunuel

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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