Relationship between inner and outer radius of a two concentric circles

In summary, to calculate the outside radius of the larger circle, you simply add the known radius of the inside circle to the difference between the two radii: \(R = r + k\). No, I did not draw a picture.
  • #1
otlconcepts
1
0
If i have two circles that say 24" apart from each other. one inside the other.
and i know the radius of the inside circel, how can i calculate the outside radius
 
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  • #2
Did you draw a picture?

[TIKZ]
\draw[thick,red] (0,0) circle (4);
\draw[->,thick,red] (0,0) -- (4, 0) node[below, xshift=-1cm] {$r_2$};
\draw[thick,blue] (0,0) circle (2);
\draw[->, thick, blue] (0,0) -- (2, 0) node[below, xshift=-0.75cm] {$r_1$};
[/TIKZ]

$r_2 - r_1 = 24"$ right? And you know $r_1$.
 
Last edited:
  • #3
Hello, and welcome to MHB! :)

Suppose \(r\) is the radius of the inner circle and \(R\) is the radius of the inner circle, where \(k\) is the difference between the two radii:

\(\displaystyle R-r=k\)

mhb_0015.png
 

1. What is the formula for calculating the area of a two concentric circles?

The formula for calculating the area of a two concentric circles is A = π(R^2 - r^2), where A is the area, π is the mathematical constant pi, R is the outer radius, and r is the inner radius.

2. How does the inner radius affect the area of a two concentric circles?

The inner radius has a direct impact on the area of a two concentric circles. As the inner radius increases, the area decreases, and vice versa. This is because the larger the inner radius, the smaller the area between the two circles.

3. What is the relationship between the inner and outer radius of a two concentric circles?

The inner and outer radius of a two concentric circles are directly related. As the inner radius increases, the outer radius also increases in order to maintain the same distance between the two circles. Similarly, if the inner radius decreases, the outer radius will also decrease.

4. How does the area of a two concentric circles change when the inner radius is equal to the outer radius?

When the inner radius is equal to the outer radius, the two circles become one and the area between them becomes zero. This means that the area of the two concentric circles is equal to the area of a single circle with the same radius.

5. Can the inner radius of a two concentric circles be larger than the outer radius?

No, the inner radius of a two concentric circles cannot be larger than the outer radius. This would result in the circles overlapping, which would not be considered concentric circles. The inner radius must always be smaller than the outer radius in order for the circles to be concentric.

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