Finding the Radius of the Larger Circle

Oct 13, 2025 by talynt.org 148 views

**The Ratio of Circle Diameters: A Mathematical Exploration**

In mathematics, the study of circles and their properties is a fundamental concept that has numerous applications in various fields. One of the key properties of circles is their circumference, which is the distance around the circle. In this article, we will explore the relationship between the diameters of two circles and their circumferences, using the given ratio of 3:5 and the circumference of the larger circle.

We are given that the ratio of the diameters of two circles is 3:5. This means that if the diameter of the larger circle is 5 units, the diameter of the smaller circle is 3 units. We are also given that the circumference of the larger circle is approximately 113.1 mm. Our goal is to find the approximate circumference of the smaller circle.

The formula for the circumference of a circle is given by:

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Finding the Radius of the Larger Circle

We are given that the circumference of the larger circle is approximately 113.1 mm. We can use the formula for circumference to find the radius of the larger circle:

113.1 = 2πr

To solve for r, we can divide both sides of the equation by 2π:

r = 113.1 / (2π) r ≈ 18.0 mm

Finding the Diameter of the Larger Circle

The diameter of a circle is twice its radius. Therefore, the diameter of the larger circle is:

d = 2r d ≈ 2(18.0) d ≈ 36.0 mm

Finding the Radius of the Smaller Circle

We are given that the ratio of the diameters of the two circles is 3:5. This means that the diameter of the smaller circle is 3/5 of the diameter of the larger circle:

d_small = (3/5)d_large d_small ≈ (3/5)(36.0) d_small ≈ 21.6 mm

The radius of the smaller circle is half its diameter:

r_small = d_small / 2 r_small ≈ 21.6 / 2 r_small ≈ 10.8 mm

Finding the Circumference of the Smaller Circle

We can use the formula for circumference to find the circumference of the smaller circle:

C = 2πr C ≈ 2π(10.8) C ≈ 67.9 mm

In this article, we explored the relationship between the diameters of two circles and their circumferences, using the given ratio of 3:5 and the circumference of the larger circle. We found that the approximate circumference of the smaller circle is 67.9 mm.

Q: What is the ratio of the diameters of the two circles? A: The ratio of the diameters of the two circles is 3:5.

Q: What is the circumference of the larger circle? A: The circumference of the larger circle is approximately 113.1 mm.

Q: What is the diameter of the larger circle? A: The diameter of the larger circle is approximately 36.0 mm.

Q: What is the radius of the smaller circle? A: The radius of the smaller circle is approximately 10.8 mm.

Q: What is the circumference of the smaller circle? A: The circumference of the smaller circle is approximately 67.9 mm.

Q: What is the ratio of the circumferences of the two circles? A: The ratio of the circumferences of the two circles is 3:5.

Q: How do you find the circumference of a circle? A: The formula for the circumference of a circle is given by C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Q: What is the relationship between the diameter and the circumference of a circle? A: The diameter of a circle is twice its radius, and the circumference of a circle is given by the formula C = 2πr.