Question

how far does the tip of an hour hand on a clock move in 3hours if the hour hand is 2cm long?

Answer 1

This is a pythagoras problem that you have to tackle like this\[c=\sqrt{(2cm)^{2}+(2cm)^{2}}=2\sqrt{2}cm\]Or are you asking for the arc length and not the hypothenuse?

Answer 2

i think i need the arc length

Answer 3

Then you have to find the circunference of the clock and then divide it by four since the needle travels one fourth of the circunference.\[d=\frac{ c }{ 4 }=\frac{ 2\Pi r }{ 4 }=\frac{ \Pi r }{ 2 }=\frac{ \Pi 2cm }{ 2 }=\Pi cm=3.14......cm\]

Answer 4

so the answer would be 3.14??

Answer 5

or do i times that by 12?

Answer 6

On a unit circle, going half way around would be pi units (so 180 degrees corresponds to pi, this is where that conversion comes from). The formula for circumference is 2piR (R being radius). So on a circle with radius of 2 it would be 4pi for the entire circumference. Arc length uses the same formula, but you put in the amount of radians that corresponds with the angle.

What I mean is, draw a picture of this circle. Figure out what the angle is from the starting point to the ending point and put that amount into the formula instead of pi.

Answer 7

the tip of the hour hand describes a quarter of the circumference of a circle in 3 hours
radius of circle is 2 cms

so distance travelled = 1/4 * 2 pi r = (1/4) * 2 * pi * 2

Answer 8

Yeah the answer is 3.14 cm or more especifically\[\Pi cm\]

Answer 9

right

Answer 10

o ok