Tyra bought a lollipop with a diameter of 2 1/2 inches. What is the circumference of the lollipop to the nearest tenth of an inch?
Understand the Problem
The question is asking to calculate the circumference of a lollipop given its diameter of 2 1/2 inches. To solve this, we will use the formula for circumference, which is C = πd, where 'd' is the diameter.
Answer
The circumference is approximately $7.9$ inches.
Answer for screen readers
The circumference of the lollipop is approximately (7.9) inches.
Steps to Solve
- Convert the diameter to an improper fraction
The diameter of the lollipop is given as (2 \frac{1}{2}) inches. To convert it to an improper fraction: $$ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} \text{ inches} $$
- Use the circumference formula
The formula for circumference is given by: $$ C = \pi d $$ Substituting the diameter: $$ C = \pi \times \frac{5}{2} $$
- Calculate the circumference
Using the approximate value of (\pi \approx 3.14): $$ C \approx 3.14 \times \frac{5}{2} = \frac{15.7}{2} \approx 7.85 \text{ inches} $$
- Round to the nearest tenth
To round (7.85) to the nearest tenth, we look at the hundredths place, which is (5): $$ 7.85 \approx 7.9 $$
The circumference of the lollipop is approximately (7.9) inches.
More Information
The circumference calculated gives the distance around the lollipop. Using the diameter is a direct application of the formula, which can be applied to any circular object.
Tips
- Mistake in converting mixed numbers: Ensure that mixed numbers are properly converted into improper fractions for accuracy.
- Misapplication of (\pi): Sometimes, students may use incorrect values for (\pi); it's crucial to use a consistent approximation, typically (3.14).
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