Two concentric circles with centre 0 and radius r and r respectively.if r=3r,express the area ofthe shaded part in terms of Pie and r
So much wrong with this post.
You have 2 circles with the same centre and "radius r and r" , makes
no sense.
then: "if r=3r" ???? , not possible unless r = 0. That's like saying 5 = 15
then: Pie !! Is that an apple or a blueberry pie. You meant pi or π
Anyway, my interpretation of that gibberish is that you have 2
circles with the same centre and the larger circle has a radius which
is three times that of the smaller.
Area of larger circle = 9πr^2
area of smaller circle = πr^2
Depending on what is shaded, you don't say, do the appropriate
calculation. My guess would be that you want 8πr^2, the "ring" formed
by the larger and the smaller circles.
To find the area of the shaded part, we need to subtract the area of the smaller circle from the area of the larger circle.
Area of a circle is given by the formula A = πr^2, where r is the radius.
Let's denote the radius of the smaller circle as r1 and the radius of the larger circle as r2.
Given r2 = 3r1, we can substitute this value into the area formulas.
Area of the smaller circle = πr1^2
Area of the larger circle = πr2^2
Substituting r2 = 3r1:
Area of the larger circle = π(3r1)^2 = π(9r1^2)
Therefore, the shaded area = Area of the larger circle - Area of the smaller circle
= π(9r1^2) - πr1^2
Factoring out πr1^2:
= πr1^2(9 - 1)
Since r1 is the radius of the smaller circle, which is also the radius of the shaded part,
we can represent r1 as r in our final answer.
Therefore, the area of the shaded part = πr^2(9 - 1)
= πr^2(8)
= 8πr^2
So, the area of the shaded part is expressed as 8πr^2.
To express the area of the shaded part in terms of π and r, we first need to find the areas of both circles.
The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
For the larger circle with radius r, the area is A1 = πr^2.
For the smaller circle with radius 3r, the area is A2 = π(3r)^2 = π(9r^2) = 9πr^2.
To find the shaded area, we need to subtract the area of the smaller circle from the area of the larger circle. Therefore, the shaded area (A) is given by:
A = A1 - A2 = πr^2 - 9πr^2 = (-8πr^2).
So, the area of the shaded part, in terms of π and r, is (-8πr^2).