Radius of Each Circle

[harpazo]

Two circles have circumferences that add up to 12pi cm and areas that add up to 20pi square cm. Find the radius of each circle.

Solution:

Circumference of a circle is 2pi•r.

Area of circle is pi•r^2.

Stuck here....

 

[pka]

Two circles have circumferences that add up to 12pi cm and areas that add up to 20pi square cm. Find the radius of each circle.

From the given:
\(\displaystyle 2 \pi R_1+2 \pi R_2=12 \pi\)

\(\displaystyle \pi R_1^2+\pi R_2^2=20\pi \)

Can you solve that system?

 

[harpazo]

From the given:
\(\displaystyle 2 \pi R_1+2 \pi R_2=12 \pi\)

\(\displaystyle \pi R_1^2+\pi R_2^2=20\pi \)

Can you solve that system?

Yes, I can solve the system. No problem. I simply want to know what information in the application helped you create the system of equation? Can you break that process down one sentence at a time? Thanks.

 

[Otis]

… I simply want to know what information in the [OP] helped you create the system of [equations] …

Well, speaking simply, ALL of the given information. Let's look at that, again:

Two circles have circumferences that add up to 12pi cm and areas that add up to 20pi square cm. Find the radius of each circle.

The parts in red tell us there are two circles, and we are to determine the radius of each.

As in all word problems, we start by assigning symbols to represent what we're trying to find. In this exercise, we are trying to find two radii. So we pick symbols to represent them.

Let R₁ = radius of the first circle

Let R₂ = radius of the second circle

Is the system of equations posted by pka clear now? If not, ask yourself the following questions about the circumferences and the areas.

R₁ represents the radius of the first circle, so what expression represents the circumference?

R₂ represents the radius of the second circle, so what expression represents the circumference?

The green part tells us those two circumference expressions add up to 12pi.

R₁ represents the radius of the first circle, so what expression represents the area?

R₂ represents the radius of the second circle, so what expression represents the area?

The blue part tells us those two area expressions add up to 20pi.

?

 

[hoosie]

 

[harpazo]

Thank you everyone.