The circumference of a soup bowl is 42 centimeters. What is the approximate length of its radius?
Understand the Problem
The question is asking for the radius of a soup bowl given its circumference. We can use the formula for the circumference of a circle, which is C = 2πr, to find the radius.
Answer
The approximate length of the radius is $6.5 \, \text{cm}$.
Answer for screen readers
The approximate length of the radius is $6.5 , \text{cm}$.
Steps to Solve
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Identify the formula for circumference
The formula for the circumference ( C ) of a circle is given by: $$ C = 2\pi r $$ where ( r ) is the radius.
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Substitute the known value
Given that the circumference ( C ) is 42 centimeters, we can substitute that into the equation: $$ 42 = 2\pi r $$
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Solve for the radius ( r )
To isolate ( r ), divide both sides by ( 2\pi ): $$ r = \frac{42}{2\pi} $$
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Calculate the numerical value of the radius
Using an approximate value for ( \pi ) (about 3.14), we can calculate ( r ): $$ r \approx \frac{42}{2 \times 3.14} $$ $$ r \approx \frac{42}{6.28} $$ $$ r \approx 6.68 , \text{cm} $$
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Round the result
Rounding 6.68 cm gives approximately ( 6.5 , \text{cm} ).
The approximate length of the radius is $6.5 , \text{cm}$.
More Information
The radius is half the diameter of a circle, and it is directly related to the circumference by the formula ( C = 2\pi r ). Knowing the circumference allows you to find the radius using basic algebra.
Tips
- Forgetting to divide by ( 2\pi ): Some may mistakenly use the full circumference value without dividing it correctly to find the radius. Always isolate ( r ) by dividing both sides by ( 2\pi ).
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