a circle has a circumference of 185mm. find the area of the sector cut off by an angle of pi/5 subtended at the centre
2007-08-12 19:02:57 · 8 answers · asked by loza 2 in Science & Mathematics ➔ Mathematics
could you please put the answer in radians
thanks
2007-08-12 19:42:48 · update #1
area = (1/2)θr^2 = (1/2)(pi/5)185^2 mm^2
2007-08-12 19:12:54 · answer #1 · answered by sahsjing 7 · 1⤊ 2⤋
First we should find the area of the whole circle. From the circumference, we need to find the radius of the circle, and then we can calculate the area.
C = 2pi * R
R = C / 2pi
R = 185mm / 2pi
R = 29.44 mm
A = pi * R^2
A = pi * (29.44mm)^2
A = 2723.5 mm^2
If a total circle encircles 2pi radians, then the area of a pi/5 radian sector would be in proportion to the angle of the sector to the whole circle.
A(total) / 2pi = A(sector) / pi/5
A(sector) = pi/5 / 2pi * 2723.5
A(sector) = 272.35 mm^2
2007-08-12 19:14:03 · answer #2 · answered by Anonymous · 0⤊ 1⤋
pi times diameter = 185.
So your radius is 185/2pi =29.46 mm.
pi/5 is a tenth of 2pi which corresponds to 360 degrees of the circle. So the angle of your sector is 0.628 radians.
Therefore the area of the sector = angle x radius^2/2 =272.52square mm.
2007-08-12 19:21:09 · answer #3 · answered by stvenryn 4 · 0⤊ 2⤋
Area of circle = A = π r ²
Circumference = C = 2 π r
2 π r = 185
r = 185 / 2 π
Area of circle = A = π x 185 ² / 4 π ²
A = 185 ² / (4 π)
A = 2723.5 mm ²
Area of sector = As = 2723.5 (π/5 /2π) mm ²
As = (1/10) x 2723.5 mm ²
As = 272.35 mm ²
2007-08-12 19:51:18 · answer #4 · answered by Como 7 · 1⤊ 0⤋
Unfortunately, the other answers on this page are incorrect. First, you need to find the radius of the circle. The circumference is equal to 2 * pi * r, where r is the radius of the circle. But, you also know that the circumference is equal to 4.5 * (360 / 30) = 54, and so the radius is 54 / (2 * pi) = 8.59cm, to two decimal places. So, the area is equal to pi * r^2 = pi * (8.59)^2 = 232.05cm^2, to two decimal places.
2016-05-21 03:56:14 · answer #5 · answered by ? 3 · 0⤊ 0⤋
first we find the radius of the circle
C= 2 x pi x r
185 = 2 x 3.14 x r
r = 29.46mm
now we find the area of the whole circle
A = pi x r^2
A =3.14 x (29.46)^2
A =2725.18 mm^2
now this area is subtenede by and angle of 2pi so an angle of pi/5 would subtend:
=(2725.18 x pi/5)/ 2pi
= 272.52 mm^2
2007-08-12 19:15:44 · answer #6 · answered by Southpaw 5 · 0⤊ 1⤋
First you need to find the radius to put it into the equation for a sector. Use the fact that C = 2pi r.
I think (check your textbook) that the formula for a sector (when your angle theta is in radians) is:
Area = theta/2 *r^2.
Good luck!
2007-08-12 19:17:06 · answer #7 · answered by douglas 2 · 0⤊ 2⤋
L /185 =( π/5)/(2π) THEN L = 18.5 mm
2007-08-13 06:39:41 · answer #8 · answered by mramahmedmram 3 · 0⤊ 1⤋