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655-705 (Hard)|   Geometry|      
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Bunuel
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The hour hand of a clock is 3 feet long. How many feet does the tip of 01 Dec 2020, 10:45
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55% (hard)

Question Stats:

60% (01:41) correct 40% (01:52) wrong based on 65 sessions

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The hour hand of a clock is 3 feet long. How many feet does the tip of this hand move between 9:30 P.M. and 1:30 A.M. the following day?

(A) π
(B) 2π
(C) 3π
(D) 4π
(E) 24π
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B
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UsamaGuddar
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The hour hand of a clock is 3 feet long. How many feet does the tip of 01 Dec 2020, 10:55
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Can we safely assume that the hour hand is equal to the radius of the circles?

If so, the answer is 4 times circumference = 24 pi

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TestPrepUnlimited
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The hour hand of a clock is 3 feet long. How many feet does the tip of 01 Dec 2020, 15:37
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Bunuel
The hour hand of a clock is 3 feet long. How many feet does the tip of this hand move between 9:30 P.M. and 1:30 A.M. the following day?

(A) π
(B) 2π
(C) 3π
(D) 4π
(E) 24π
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We can write 1:30 a.m. as 13:30 a.m. just to do the subtraction, so we know 13-9 = 4 hours have passed. The hour hand moved 4 circumferences in total, each circumference is \(2*\pi*r = 2\pi*3 = 6\pi\) so in total it is \(24\pi\).

Ans: E
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The hour hand of a clock is 3 feet long. How many feet does the tip of 01 Dec 2020, 22:54
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are you sure? i guess only minute hand will move that much. hour hand will be on 1 finally.
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harsh1111
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The hour hand of a clock is 3 feet long. How many feet does the tip of 02 Dec 2020, 05:28
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I think the hour hand will move 1/12*360= 30° in 1 hour so it will move 120° in 4 hours which is 2πr/3 = 2*π*3/3 = 2π

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UsamaGuddar
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The hour hand of a clock is 3 feet long. How many feet does the tip of 02 Dec 2020, 05:30
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Harsh I think your confusing the area covered w distance travelled

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urmi760
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The hour hand of a clock is 3 feet long. How many feet does the tip of 02 Dec 2020, 05:55
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The correct answer is B (2pi).

In one hour, an hour hand moves 30 degrees (360/12), so in 4 hours it will move by 120 degrees.

Distance travelled by the tip of an hour hand = 120/360 * 2 * pi * r = 1/3 * 2 *pi * 3 = 2*pi
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The hour hand of a clock is 3 feet long. How many feet does the tip of 23 Jul 2024, 02:55
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You can visualise it this way:

The circumference of a clock can be divided into 12 equal parts. So we can say that the hour hand moved 4 parts out of total 12 parts, OR 4 hours out of total 12 hours.

Therefore our answer is \(\frac{4}{12}*circumference\)

Radius \(= 3\), so circumference is \(6π\)

\(\frac{4}{12}*6n = 2n­\)­
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