The area of a circle is given by the formula A+pier^2, where r is the radius. If increasing the radius of a circle by 1 inch gives the resulting circle an area of 100pie square inches, what is the radius of the original circle?
9 inches.
Idk,,, bruh lol its 49.5 durr cuz 49.5*2= 99 +1 ( increased area) = 100 pi or original radius.
Let's start solving the problem step by step.
1. We know that the area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
2. In this problem, we are given that increasing the radius of a circle by 1 inch gives the resulting circle an area of 100π square inches.
3. So, the area of the new circle is 100π square inches.
4. We also know that the area of the new circle is given by the formula A = π(new radius)^2.
5. Since the new radius is the original radius plus 1 inch, we can write the equation as 100π = π(original radius + 1)^2.
6. Now we can solve the equation for the original radius.
- Divide both sides of the equation by π to get rid of it: 100 = (original radius + 1)^2.
- Take the square root of both sides to isolate the original radius + 1: √100 = original radius + 1.
- Simplifying the square root, we get 10 = original radius + 1.
- Subtracting 1 from both sides, we find that the original radius is 10 - 1 = 9 inches.
7. Therefore, the radius of the original circle is 9 inches.
To find the radius of the original circle, we can use the equation for the area of a circle and solve for r.
Let the radius of the original circle be denoted as r.
According to the given information, increasing the radius of the original circle by 1 inch results in a new circle with an area of 100π square inches.
The formula for the area of a circle is A = πr^2.
So, the area of the larger circle can be expressed as (100π) = π(r + 1)^2.
First, we can simplify the equation by dividing both sides by π:
100 = (r + 1)^2.
Next, we can take the square root of both sides to solve for r + 1:
√100 = √(r + 1)^2.
10 = r + 1.
Now, we can solve for r by subtracting 1 from both sides:
10 - 1 = r + 1 - 1.
9 = r.
Therefore, the radius of the original circle is 9 inches.