In order 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 9.42 centimeters?

Question

Question 17 options:

A)

6 centimeters

B)

3 centimeters

C)

1.5 centimeters

D)

4 centimeters

Answer 1

To find the size of the buttonhole needed for a button with a circumference of 9.42 centimeters, we first need to calculate the diameter of the button. The relationship between the circumference (C) and the diameter (D) of a circle is given by the formula:

\[ C = \pi \times D \]

We can rearrange this formula to solve for the diameter:

\[ D = \frac{C}{\pi} \]

Now, substituting the given circumference:

\[ D = \frac{9.42}{\pi} \]

Using \( \pi \approx 3.14 \):

\[ D \approx \frac{9.42}{3.14} \approx 3.0 \text{ centimeters} \]

Thus, the diameter of the button is approximately 3 centimeters.

Since the buttonhole needs to be the same size as the button's diameter, the required size of the buttonhole is:

3 centimeters

Looking at the options provided, the answer is:

B) 3 centimeters