Question

a circle with radius 3 centimeters is cut from a square piece of felt. the sides of the felt square are 8 centimeters long. how much felt is left over? use 3.14 for π. show your work.

Explanation:

Step1: Calculate the area of the square

The area formula of a square is $A = s^2$, where $s$ is the side - length. Given $s = 8$ cm, so $A_{square}=8^2=64$ $cm^2$.

Step2: Calculate the area of the circle

The area formula of a circle is $A=\pi r^2$. Given $r = 3$ cm and $\pi=3.14$, so $A_{circle}=3.14\times3^2=3.14\times9 = 28.26$ $cm^2$.

Step3: Calculate the remaining area

The remaining area $A_{remaining}=A_{square}-A_{circle}$. Substitute the values of $A_{square}$ and $A_{circle}$ into the formula: $A_{remaining}=64 - 28.26=35.74$ $cm^2$.

Answer:

$35.74$ $cm^2$