Question

1. find the difference between the area and the circumference of the circle shown below. leave your answer in terms of π. diagram of a circle with a vertical dashed line labeled 16 answer: ______

Explanation:

Step1: Determine the radius of the circle

The diameter of the circle is given as 16, so the radius \( r=\frac{16}{2} = 8\).

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A=\pi r^{2}\). Substituting \( r = 8\), we get \( A=\pi\times8^{2}=64\pi\).

Step3: Calculate the circumference of the circle

The formula for the circumference of a circle is \( C = 2\pi r\). Substituting \( r=8\), we get \( C=2\pi\times8 = 16\pi\).

Step4: Find the difference between area and circumference

We need to find \( A - C\). Substituting the values of \( A\) and \( C\), we have \( 64\pi-16\pi=48\pi\).

Answer:

\( 48\pi \)