Question

find the radius of the button.
radius: □ in.

(image of a button with a measurement of 3\frac{1}{2} in. indicating the diameter)

Explanation:

Step1: Identify the diameter

The given length \( 3\frac{1}{2} \) in is the diameter (\( d \)) of the button (a circle). First, convert the mixed number to an improper fraction: \( 3\frac{1}{2}=\frac{7}{2} \) in.

Step2: Use the radius formula

The formula for the radius (\( r \)) of a circle is \( r=\frac{d}{2} \). Substitute \( d = \frac{7}{2} \) into the formula: \( r=\frac{\frac{7}{2}}{2}=\frac{7}{2}\times\frac{1}{2}=\frac{7}{4}=1\frac{3}{4} \) in.

Answer:

\( 1\frac{3}{4} \) (or \( \frac{7}{4} \))