r = 17/pi cm
A = 3420/13 m^2
Step-by-step explanation:
The formula for circumference is 2*pi*r where r is the radius. so we don't know radius, but we know the answer to the equation.
2*pi*r = 34 Just use algebra to solve for r. To explain it simply divide both sides by 2*pi
r = 34/(2*pi)
r = 17/pi just enter that into your calculator
The next question is actually a little tricky. you just need to know if you have some percent of a circle, you have that same percent of the area. so if you cut a circle in half, or in other words had an arc of 180 degrees, you would have half the total area. Or, more applicable to this question, if you have the area of an arc of 180, if you double it you get the area of the whole 360 degree circle.
Now, knowing this we see the question gives us the area of an arc that has 117 degrees. We want to know what percent this is of 360, then we can multiply it by an appropriate number to find the full circle. Again, if you had 180 degrees we would multiply by 2 because 180 is 1/2 of 360. if we had 90 we would multiply by 4 because 90 is 1/4 of 360. So we need to find that for 117. to do this just make a fraction of what we have divided by 360
117/360
Now, you could simplify it, or just keep it the same. For the record it simplified to 13/40. Anyway, the trick is to determine what you have to multiply the fraction by to get 1. Just in case you think it's 360 I want to clarify. yes you only had to multiply 1/2 by 2, but that's because 1 was in the numerator. it would be more accurate to say you multiply by 2/1. You basically flip the fraction. so here you multiply by 360/117 or 40/13.
Finally, this is what you multiply the area given for the one sector by. so it says that arc has an area of 85.5. So just multiply by 40/13.
85.5 * 40/13
3420/13
So just enter that into your calculator and it will give you the decimal answer.
Let me know if any of this was hard to follow and i would be happy to explain hopefully better.
