Question : if there is a quarter circle that measures 4 on both straight lines, what would be the perimeter of the quarter circle?
if there is a semi circle that the straight line measures 6, what would be the perimeter of the semicircle? please explain to me the whole process for both.
Answer : A quarter circle has an arc length that is 1/4 of the circumference. The radius is the straight side of this. So
P = 1/4*2* *4 + 4 + 4 (you have to add the arc plus the 2 straight sides)
P = 2 + 8
For the semi-circle, it is 1/2 the circumference, and if the straight side is 6, the radius is 3, so:
P = 1/2 * 2* *3 + 6
P = 3 + 6
Question : since pi = circumference of circle / diameter, would it be more accurate to calculate the area of the circle by substituting the values of circumference of the circle over it's diameter as the pi value rather than using the actual value of pi?
please also explain what is pi to me in a simpler way, i don't get it reading from the net... thanks!!
Answer : You could do that if you wanted...in fact, you could work out what the formula for area was in terms of circumferance:
circum = pi * 2 * radius
area = pi * radius^2
area = (circum/2r) * r^2
area = (circum * r)/2
This is why pi is very important in math. Look at the world around you. Do you notice that somethings in the world are straight lines and somethings are circles? Its important to be able to translate between the linear world and circular world.
The whole reason pi came about was from the the need to do this translation. So for example, when someone designed a wheel that was a foot in diameter, it became important to know how far it would travel after one revolution - that is the circumference. See, circumference is circular motion. Diameter is linear.
The beautiful thing is that every circle in the world has the exact same ration between its circum and its radius. So as long as that ratio is the same, people gave it the name of a very tasty food. :-)
Question : Point 0 is the center of the pair of concentric circles, and the shaded area is 1/6 the area of the outer circle, Determine the value of x?
The picture of the problem is at:
(# 24 is where it is on the calender)
If you can explain it too that would be a lot of help :)
P.S. the answer isnt 60 degrees!
Answer : The outer circle has radius 4 so its area is 16 pi
The shaded area is the area of the sector minus the unshaded part. To get that, make a proportion: x/360 = sector/16 pi
so the sector = 16x pi / 360
and the iner circle has area 1 pi so the area of the unshaded part is
x/360 = unshaded/ 1pi so unshaded = 1x pi / 360
subtract to get shaded = 15x pi / 360 which reduces to x pi / 24.
multiplied by 6 [since it's 1/6 the whole area] comes out x pi / 4
So you know x pi / 4 = 16 pi making x pi = 4(16 pi) = 64 pi so x = 64
Hope that makes sense and I didn't do any arithmetic mistakes (no calculator here)