For a button to fit through its buttonhole, the hole needs to be the size of the button’s diameter. What size buttonhole is needed for a button with a circumference of 7.38 centimeters? (Use the value of 3.14 to represent pi.) A. 2.35 centimeters B. 1.14 centimeters C. 5.14 centimeters D. 3.69 centimeters
The correct answer and explanation is:
To determine the diameter of a button given its circumference, we use the formula: Circumference=π×Diameter\text{Circumference} = \pi \times \text{Diameter}
We are given:
- Circumference = 7.38 centimeters
- π=3.14\pi = 3.14
Rearranging the formula to solve for the diameter: Diameter=Circumferenceπ=7.383.14\text{Diameter} = \frac{\text{Circumference}}{\pi} = \frac{7.38}{3.14}
Now calculate: 7.383.14≈2.35 centimeters\frac{7.38}{3.14} \approx 2.35 \text{ centimeters}
✅ Correct Answer: A. 2.35 centimeters
🧠 Explanation (300 words):
The question involves converting the circumference of a button into its diameter so we can determine the size of the buttonhole needed for it to pass through.
The circumference of a circle is directly related to its diameter through the formula: C=π⋅dC = \pi \cdot d
Where:
- CC is the circumference
- π\pi is approximately 3.14
- dd is the diameter
To find the diameter, we isolate dd: d=Cπd = \frac{C}{\pi}
We are told that the circumference of the button is 7.38 cm. Plugging this into the formula: d=7.383.14≈2.35 cmd = \frac{7.38}{3.14} \approx 2.35 \text{ cm}
This tells us that the buttonhole must be at least 2.35 cm wide to allow the button to pass through.
This is a practical use of math in daily life. When making clothing or crafts, knowing how to convert between circumference and diameter ensures parts will fit together properly. If the hole were too small (using one of the other answer options like 1.14 cm), the button wouldn’t fit. If it’s too large, the button might slip out.
Thus, Option A: 2.35 centimeters is the correct and precise answer based on the formula and given values.