|
Question 965752: Please help me solve this question:A cone with the sector angle of 45 degree is cut out of a circle of radius rcm.Find the base radius of the cone.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you cut out a sector of 45 degrees from the larger circle.
the length of the arc of that sector is equal to 1/8 times the circumference of the larger circle.
this is because arc length = 45/360 * 2*pi*r which makes arc length equal to 1/8 * 2*pi*r.
the arc length of the sector that you just cut out is the circumference of the base circle of the cone.
since the circumference of the base circle of the cone is 1/8 times the circumference of the larger circle, then it stands to reason that the radius of the base circle of the cone should be equal to 1/8 times the radius of the larger circle.
let r1 = the radius of the base circle of the cone.
let r2 = the radius of the larger circle.
c1 = circumference of the base circle of the cone.
c2 = circumference of the larger circle.
c1 = 2*pi*r1
c2 = 2*pi*r2
since c2 is equal to 8 times c1, we get:
c1/c2 = 1/8 = (2*pi*r1) / (2*pi*r2)
since 2*pi in the numerator and denominator are the same, then cancel out, andyou are left with:
c1/c2 = 1/8 = r1/r2
the ratio of the circumference of the base circle to the larger circle is equla to 1/8 and the ratio of the radius of the base circle to the radius of the larger circle is also 1/8.
i believe that's what you're asking.
if it's any different, let me know.
|
|
|
| |
