concentric circles

[sa^phir12]

Hello I need help for a problem that I can not resolve
In the problem they say that a family organizes a dart tournament. The target is composed of three concentric circles. The radius of the large circle (1 point) is 25 cm and the radius of the small circle (10 points) is 10 cm. What is the radius of the middle circle (5 points area) to reach the 5 points area is 35.84%

Thank you in advance

 

[Deleted member 4993]

Hello I need help for a problem that I can not resolve
In the problem they say that a family organizes a dart tournament. The target is composed of three concentric circles. The radius of the large circle (1 point) is 25 cm and the radius of the small circle (10 points) is 10 cm. What is the radius of the middle circle (5 points area) to reach the 5 points area is 35.84%

Thank you in advance

Are the areas of the annular regions proportional to the assigned points?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[sa^phir12]

I do not think that the annular regions are proportionate to the points awarded because it is not specified in the text. But regarding my approach I started by finding the surface of each zone because I think it will help me finding the radius.The surface of the large circle is pi x ( Radius )²=1963.5.
After the surface of the small circle is pi x ( Radius )²=314.16
But I can’t find the radius of the middle circle and then find the surface of the middle circle. I thought that the radius of the surface of the middle circle to the total surface gives the probability of reaching the area of 5 points(mean circle)=35.84%

From this equation I made the following equation: pi x (Radius) ² / pi x (Radius) ² + 314.16 + 1965.5=35.84%
After I do an inverse equation to find the radius, but I am not sure of my approach. Do you think it is correct and will help me find the right radius?

Thank you in advance

 

[sa^phir12]

The problem is that the radius gives me 816,31cm and it's pretty weird

 

[tkhunny]

Why not be systematic and deliberate?

Largest Total Area: $$\pi(25\;cm)^2 = 1,963.5\;cm^{2}$$
Middle Annular Area: $$1,963.5\cdot 0.35 = 687.2\;cm^{2}$$
Smallest Total Area: $$\pi(10\;cm)^2 = 314.2\;cm^{2}$$
Middle Total Area: $$687.2\;cm^{2} + 314.2\;cm^{2} = 1,001.4\;cm^{2}$$
Middle Radius: You tell us?

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If you just slap stuff up and don't document what you are doing, you get things like the following:

"pi x (Radius) ² / pi x (Radius) ² + 314.16 + 1965.5=35.84% "

A Ratio + An Area + An Area = A Ratio -- Why would that ever lead to anything useful?

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Note #1 - Don't use "Surface Area" when Area will do. We don't care if the dart board has a 3 dimensional shape. We're only talking about the area of the face.

Note #2 - You should decide up front about decimal places and precision. In your version, why is the largest circle 1,963.5 and the smallest circle is 314.16? Did you DELIBERATELY select 5 significant figures?

 

[sa^phir12]

Ok thank you very much for your help i will retry the problem to see

 

[Steven G]

You have 3 concentric circles.

The smaller circle has an area of ??
The larger circle has an area of??

So the middle circle has an area of??

What do you do with this information? What is the total percentage of the middle circle to the large circle? So what is the radius of that middle circle?