Which ratio is closest to the value of pi?
Understand the Problem
The question provides a table of information about a circle (radius, diameter, circumference, and area). It asks which of the given ratios is closest to the value of pi (π). Since π is related to circumference and diameter by the formula (C = \pi d), one way of working this out is to find the value of the (\frac{C}{d}) ratio.
Answer
$\frac{18.85}{6}$
Answer for screen readers
$\frac{18.85}{6}$
Steps to Solve
- Recall the relationship between circumference, diameter, and π
The circumference $C$ of a circle is related to its diameter $d$ by the formula $C = \pi d$. Therefore, $\pi = \frac{C}{d}$.
- Calculate the value of each ratio
We need to calculate each ratio to find the one closest to $\pi \approx 3.14159$.
- Ratio 1: $\frac{6}{3} = 2$
- Ratio 2: $\frac{18.85}{3} \approx 6.283$
- Ratio 3: $\frac{28.27}{6} \approx 4.712$
- Ratio 4: $\frac{18.85}{6} \approx 3.142$
- Compare the ratios to π
Now we compare the calculated ratios to the value of $\pi \approx 3.14159$.
- $|2 - 3.14159| = 1.14159$
- $|6.283 - 3.14159| = 3.14141$
- $|4.712 - 3.14159| = 1.57041$
- $|3.142 - 3.14159| = 0.00041$
- Identify the closest ratio
The ratio $\frac{18.85}{6} \approx 3.142$ is the closest to the value of $\pi$ because it has the smallest difference.
$\frac{18.85}{6}$
More Information
The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, and it is approximately equal to 3.14159.
Tips
A common mistake could be dividing the circumference by the radius instead of the diameter. Also, calculation errors when finding the ratios could occur.
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