Find The Diameter Of A Circle With An Area Of 706.9 In². Round Your Answer To The Nearest Inch.A. 12 Inches B. 30 Inches C. 15 Inches D. 9 Inches
Understanding the Relationship Between Area and Diameter
The area of a circle is directly proportional to the square of its diameter. This relationship can be expressed using the formula:
A = πr^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Finding the Radius from the Given Area
Given that the area of the circle is 706.9 in², we can use the formula to find the radius:
706.9 = πr^2
To solve for r, we can divide both sides of the equation by π:
r^2 = 706.9 / π
r^2 = 706.9 / 3.14159
r^2 = 225.0
Taking the square root of both sides of the equation gives us the radius:
r = √225.0
r = 15.0
Finding the Diameter from the Radius
Now that we have the radius, we can find the diameter by multiplying the radius by 2:
diameter = 2r
diameter = 2(15.0)
diameter = 30.0
Therefore, the diameter of the circle with an area of 706.9 in² is 30 inches.
Conclusion
In this article, we used the formula for the area of a circle to find the radius and then used the radius to find the diameter. We found that the diameter of the circle with an area of 706.9 in² is 30 inches.
Answer
The correct answer is B. 30 inches.
Additional Information
The formula for the area of a circle is:
A = πr^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
The formula for the diameter of a circle is:
diameter = 2r
where r is the radius of the circle.
Practice Problems
- Find the diameter of a circle with an area of 113.1 in².
- Find the radius of a circle with an area of 254.5 in².
- Find the diameter of a circle with a radius of 8.5 inches.
Solutions
- The diameter of the circle with an area of 113.1 in² is 10 inches.
- The radius of the circle with an area of 254.5 in² is 15.5 inches.
- The diameter of the circle with a radius of 8.5 inches is 17 inches.
Circle Diameter Q&A =====================
Frequently Asked Questions About Circle Diameter
Q: What is the formula for finding the diameter of a circle?
A: The formula for finding the diameter of a circle is:
diameter = 2r
where r is the radius of the circle.
Q: How do I find the radius of a circle if I know its area?
A: To find the radius of a circle if you know its area, you can use the formula:
A = πr^2
where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Q: What is the relationship between the area and diameter of a circle?
A: The area of a circle is directly proportional to the square of its diameter. This means that as the diameter of a circle increases, its area increases at a faster rate.
Q: Can I find the diameter of a circle if I know its circumference?
A: Yes, you can find the diameter of a circle if you know its circumference. The formula for the circumference of a circle is:
C = 2πr
where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Q: How do I find the radius of a circle if I know its circumference?
A: To find the radius of a circle if you know its circumference, you can use the formula:
C = 2πr
where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Q: What is the difference between the diameter and radius of a circle?
A: The diameter of a circle is the distance across the circle passing through its center, while the radius is the distance from the center of the circle to its edge.
Q: Can I find the diameter of a circle if I know its area and circumference?
A: Yes, you can find the diameter of a circle if you know its area and circumference. You can use the formulas:
A = πr^2
C = 2πr
to find the radius and then use the formula:
diameter = 2r
to find the diameter.
Q: What are some real-world applications of finding the diameter of a circle?
A: Finding the diameter of a circle has many real-world applications, including:
- Calculating the area of a circular room or building
- Determining the size of a circular pipe or tube
- Finding the circumference of a circular object
- Calculating the volume of a circular container or tank
Conclusion
In this article, we have answered some frequently asked questions about circle diameter, including how to find the diameter of a circle if you know its area, circumference, or radius. We have also discussed the relationship between the area and diameter of a circle and some real-world applications of finding the diameter of a circle.