Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

enter image description here

How do I find out what the radius length of the angle is? The answer is D by the way.

share|improve this question

5 Answers 5

up vote 5 down vote accepted

Let the circle's circumference be given by $C$, let it's diameter = $d$, it's radius $r$.

The ratio of the arc of the circle to the circumference is equal to the ratio of the $30$ degree angle to the measure of a circle = $360^\circ$:

$$\dfrac{6}{C} = \dfrac{30}{360} = \dfrac{1}{12}\quad \implies \quad C = 6\times 12 \implies C=72$$

Using the formula for circumference of a circle: $C = d\pi = 2\pi r$, and solving for r:

$$C = 72 = 2 \pi r $$ $$\implies r = \dfrac{72}{2\pi} = \dfrac{36}{\pi}$$

share|improve this answer
    
is this off by a factor of 10? I think you meant 72 after reductions. Regards –  Amzoti Feb 15 '13 at 21:38
    
Yes, indeed!... –  amWhy Feb 15 '13 at 21:43
1  
Is this making sense, Little Jon? –  amWhy Feb 15 '13 at 21:48
    
Yes this is a valid answer Thank you! –  Little Jon Feb 15 '13 at 21:52
    
You're welcome! –  amWhy Feb 15 '13 at 21:53

The full circle has perimeter $\frac{360^\circ}{30^\circ}\cdot 6\,\mathrm m=72\,\mathrm m$. As this must equal $2\pi r$, we find $r=\frac{36}\pi\,\mathrm m$.

share|improve this answer

HINT: The circumference of a circle of radius $r$ is $\pi r$. The $30^\circ$ angle is $\frac{30}{360}=\frac1{12}$ of the total angle at the centre of the circle, so $6$ metres is $\frac1{12}$ of the circumference of the circle. The whole circumference is therefore $6\cdot12=72$ metres, which, as already noted, is $2\pi r$. Therefore $r$ is ... ?

share|improve this answer

Length of the arc is $L_\alpha = \alpha r$, so $r = \frac {L_\alpha}\alpha = \frac 6{\pi/6} = \frac {36}\pi$

share|improve this answer

The way that you can solve this is by using the following formula:

$$A=\frac{n}{360}\pi{r^2}$$

Hope that helps you out! I can't figure out how to type in the equation!

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.