The area of a circle is 113.04 in. 2. What is the radius of the circle?
The Correct Answer and Explanation is:
To find the radius of a circle when given the area, we use the formula for the area of a circle:A=πr2A = \pi r^2A=πr2
Where:
- AAA is the area
- π\piπ is approximately 3.14
- rrr is the radius
Step-by-step solution:
Given:A=113.04 in2A = 113.04 \text{ in}^2A=113.04 in2
Using the formula:113.04=3.14×r2113.04 = 3.14 \times r^2113.04=3.14×r2
To find r2r^2r2, divide both sides by 3.14:r2=113.043.14r^2 = \frac{113.04}{3.14}r2=3.14113.04r2=36r^2 = 36r2=36
Now take the square root of both sides:r=36r = \sqrt{36}r=36r=6r = 6r=6
Final Answer:
6 inches\boxed{6 \text{ inches}}6 inches
Explanation
To determine the radius of a circle when you are given its area, you must understand the relationship between the radius and the area. The formula used to calculate the area of a circle is A=πr2A = \pi r^2A=πr2, which means the area is equal to the constant pi multiplied by the square of the radius.
In this problem, the area is given as 113.04 square inches. Since pi is approximately 3.14, we substitute both the area and pi into the formula. This gives the equation 113.04=3.14×r2113.04 = 3.14 \times r^2113.04=3.14×r2. The next step is to isolate r2r^2r2 by dividing both sides of the equation by 3.14. This results in r2=36r^2 = 36r2=36. Once you have the value of r2r^2r2, you can find the radius by taking the square root of 36. The square root of 36 is 6, so the radius of the circle is 6 inches.
This process demonstrates how algebra can be used to reverse a formula and solve for a missing variable. Instead of calculating area from a known radius, we start with the area and work backward to find the radius. This kind of problem is common in geometry and helps build a solid understanding of how mathematical formulas work and how they can be rearranged to solve for different parts of a shape.
