Question

1. find the difference between the area and the circumference of the circle shown below. leave your answer in terms of π. image of a circle with radius 5 answer: ________

Explanation:

Step1: Recall formulas for area and circumference of a circle

The formula for the area \( A \) of a circle with radius \( r \) is \( A = \pi r^2 \), and the formula for the circumference \( C \) is \( C = 2\pi r \). Here, the radius \( r = 5 \).

Step2: Calculate the area

Substitute \( r = 5 \) into the area formula: \( A=\pi\times5^2 = 25\pi \).

Step3: Calculate the circumference

Substitute \( r = 5 \) into the circumference formula: \( C = 2\pi\times5=10\pi \).

Step4: Find the difference between area and circumference

Subtract the circumference from the area: \( A - C=25\pi - 10\pi = 15\pi \).

Answer:

\( 15\pi \)