If the radius of a circle is doubled and the central angle of a sector is unchanged, how is the area of the sector changed?
2006-08-06 12:53:50 · 14 answers · asked by teenyb04 2 in Science & Mathematics ➔ Mathematics
it is increased by a factor of 4
a sector is a fraction f of a circle radius r.
Area of the circle is pi * r * r
Area of the sector is f x pi x r^2
Length of radius is doubled... r2 = 2 x r
A2 is now pi x 2 x r x 2 x r
ie. 4 pi r^2
Area2 of the sector is f x 4 x pi x r^2
2006-08-06 12:59:31 · answer #1 · answered by Orinoco 7 · 0⤊ 0⤋
The area of a sector is a fraction of the area of the circle. So just think if you increase the radius of a circle, the area is 4 times the original area. Sector of new circle will thus be also 4 times the area of the old circle.
Just imagine you have two pizzas one with 8" dia (or 4" radius) and the other with 16" dia (or 8" radius). If you cut each of the pizzas into say 6 slices, in both cases the angle of the sector would be 60 degrees. However you can yourself imagine the slice of 16" dia pizza would be much bigger (infact 4 times) the slice of 8" dia pizza.
So even with the same central angle of a sector the area always depends on the radius (or diamaeter) and is proportional to the square of the radius (or diameter). If you double the radius the area (of circle itself or any of its sectors) becomes 4 times the original.
2006-08-14 09:57:26 · answer #2 · answered by LEPTON 3 · 0⤊ 0⤋
Area of sector = Area of circle times (angle at the centre divided by 360 degree)
In this case angle is not changed threfore
Area of sector is proportional to area of circle, but the are of circle depends on the square of the radius therefore area of sector will be 4 times if radius is doubled
2006-08-11 12:06:13 · answer #3 · answered by Amar Soni 7 · 0⤊ 0⤋
PI R^2 = Area of a circle (A), with PI a constant, R is the radius. R^2 means R squared.
A "sector" area (S) of any given angle (alpha, which is set constant by your assumption) is simply a portion of the area (k*A). So S = k*A = k*PI*R^2 = K*R^2; where K = constant = k*PI.
Therefore S = K*R^2; so that the area of a sector varies as the square of the radius of the circle in which the sector is embedded. In your case, when R is doubled, the area of the sector increases by four-fold.
2006-08-06 13:09:31 · answer #4 · answered by oldprof 7 · 0⤊ 0⤋
Area Of The Sector
2016-10-31 00:51:16 · answer #5 · answered by Anonymous · 0⤊ 0⤋
The sector area is quadrupled, since it is proportional to pi*r^2. That is, when you double the radius, the sector area increases by 2^2, or 4.
2006-08-11 16:11:50 · answer #6 · answered by Anonymous · 0⤊ 0⤋
I don't think that the area will change since the radius is 1/ 2 the diameter and since u would have already used that radius to find the area of the sector then the diameter would be useless.
2006-08-06 13:00:15 · answer #7 · answered by tq 3 · 0⤊ 0⤋
Yes. If the radius is doubled, the area of the sector will increase four fold.
2006-08-14 07:55:24 · answer #8 · answered by young_friend 5 · 0⤊ 0⤋
it will change by the same ratio that the entire area of a circle will change if you double the radius.
if the radius goes from 1 to 2 then, using the formula
a=pi*r^2 then r goes from 1 to 2 and r squared goes from 2 to 4
so when the radius is doubled, the area is quadrupled..
2006-08-14 10:38:37 · answer #9 · answered by Anonymous · 0⤊ 0⤋
Area quadruples when the radius doubles because you are squaring.
2006-08-06 13:08:07 · answer #10 · answered by MollyMAM 6 · 0⤊ 0⤋