Radius When Area of Expanding Circle Doubles

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In summary, "Radius When Area of Expanding Circle Doubles" refers to the distance from the center of a circle to its outer edge when the area of the circle increases by twice its original size. The radius is important because it is directly related to the area of a circle, and can be calculated by taking the square root of the doubled area divided by pi. The radius and area of a circle are directly proportional, meaning that as one increases, the other also increases. Changes in the value of pi can also affect the area of a circle.
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tandoorichicken
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What is the radius when the area in square units of an expanding circle is increasing twice as fast as the radius?
 
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Originally posted by tandoorichicken
What is the radius when the area in square units of an expanding circle is increasing twice as fast as the radius?
Start with the area of a circle (A = πr2) and take the derivative with respect to time. Then apply what's given.
 
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The radius of a circle is directly proportional to its area, meaning that as the radius increases, the area also increases. Therefore, when the area of an expanding circle doubles, the radius will also double. This is because the area of a circle is calculated using the formula A = πr², where r is the radius. So, when the area is doubled, the equation becomes 2A = πr². Solving for r, we get r = √(2A/π). This means that the radius will be √2 times the original radius, which is equivalent to doubling the radius. Therefore, when the area of an expanding circle is increasing twice as fast as the radius, the radius will be twice the original radius.
 

1. What does "Radius When Area of Expanding Circle Doubles" mean?

"Radius When Area of Expanding Circle Doubles" refers to the measurement of the distance from the center of a circle to its outer edge when the area of the circle increases by twice its original size.

2. Why is the radius important in this context?

The radius is important because it is directly related to the area of a circle. As the radius increases, so does the area. Therefore, when the area of a circle doubles, the radius also increases.

3. How is the radius calculated when the area of a circle doubles?

The radius can be calculated by taking the square root of the doubled area divided by pi. This can be represented by the equation r = sqrt(2A/pi), where r is the radius and A is the original area of the circle.

4. Can the radius of a circle double without changing the area?

No, the radius and area of a circle are directly proportional. This means that as one increases, the other also increases. Therefore, in order for the area to double, the radius must also increase.

5. Is the radius the only factor that affects the area of a circle?

No, the area of a circle is also affected by the value of pi. Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. Therefore, the area of a circle can also be affected by changes in the value of pi.

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