What is the length of the radius of a circle if the diameter is 20 centimeters?
Understand the Problem
The question is asking for the length of the radius of a circle given its diameter. To solve it, we will use the formula that the radius is half the diameter.
Answer
The radius is \( 10 \) centimeters.
Answer for screen readers
The length of the radius is ( 10 ) centimeters.
Steps to Solve
- Understand the relationship between diameter and radius
The radius of a circle is half the diameter. We can express this relationship with the formula: $$ r = \frac{d}{2} $$ where $r$ is the radius and $d$ is the diameter.
- Substitute the given diameter into the formula
We know that the diameter of the circle is 20 centimeters. Substituting this value into the radius formula gives: $$ r = \frac{20 \text{ cm}}{2} $$
- Calculate the radius
Now perform the division to find the radius: $$ r = 10 \text{ cm} $$
The length of the radius is ( 10 ) centimeters.
More Information
The radius is crucial in circle geometry, affecting properties like the area and circumference. For example, the area of a circle can be calculated using the formula ( A = \pi r^2 ).
Tips
- Confusing diameter with radius: Remember that the radius is always half of the diameter.
- Incorrect division: When calculating the radius, ensure that the division is done correctly.
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