Question

1. a circle is inscribed in a square so that the circle touches each side of the square at one point. if the perimeter of the square measures 20 cm, what is the circumference of the circle? a. $5\pi$ cm b. $10\pi$ cm c. $20\pi$ cm d. $40\pi$ cm

Explanation:

Step1: Find side length of square

Perimeter of square \( P = 4s \), where \( s \) is side length. Given \( P = 20 \) cm, so \( 20 = 4s \). Solving for \( s \), we get \( s=\frac{20}{4}=5 \) cm.

Step2: Determine diameter of circle

Since the circle is inscribed in the square, the diameter \( d \) of the circle equals the side length of the square. So \( d = 5 \) cm.

Step3: Calculate circumference of circle

The formula for circumference of a circle is \( C=\pi d \). Substituting \( d = 5 \) cm, we get \( C = \pi\times5 = 5\pi \) cm.

Answer:

a. \( 5\pi \) cm