If the diameter of a bicycle wheel is 24 inches, what is the ratio of the radius of the wheel to the diameter of the wheel?
The Correct answer and Explanation is:
The ratio of the radius of the wheel to the diameter of the wheel is 1:2.
Here’s how we arrive at this ratio:
- Understanding the relationship between radius and diameter: The diameter of a circle is defined as the distance across the circle through its center. The radius, on the other hand, is the distance from the center of the circle to any point on its edge. The radius is exactly half the length of the diameter. Mathematically, this can be expressed as:Radius=Diameter2\text{Radius} = \frac{\text{Diameter}}{2}Radius=2Diameter
- Calculating the radius: In this case, the diameter of the bicycle wheel is given as 24 inches. Using the relationship above:Radius=24 inches2=12 inches\text{Radius} = \frac{24 \text{ inches}}{2} = 12 \text{ inches}Radius=224 inches=12 inchesTherefore, the radius of the wheel is 12 inches, while the diameter remains 24 inches.
- Finding the ratio: The question asks for the ratio of the radius to the diameter. Since the radius is 12 inches and the diameter is 24 inches, we can express the ratio as:Ratio=1224=12\text{Ratio} = \frac{12}{24} = \frac{1}{2}Ratio=2412=21This means that for every 1 unit of radius, there are 2 units of diameter, or the radius is half the diameter.
- Why this is always true: This ratio holds for any circle, not just the bicycle wheel in the problem. The radius will always be half the diameter, so the ratio of radius to diameter is always 1:2 for any circle. This is a fundamental property of circles and can be useful in many applications, such as calculating the circumference or area of a circle, which involve either the radius or diameter in their formulas.
In summary, the ratio of the radius to the diameter of the wheel is 1:2, reflecting the consistent relationship between these two measurements in any circular object.