What is the approximate area that remains after a circle 3 1/2 in diameter is cut from a square piece of cloth with a side of 8''?

Calculate the area of the square cloth first. Then calculate the area of the circle. Subtract the area of the circle from the area of the square, which is the area that ramains.

Remaining area =  area of cloth - area of circle........so we have

8^2  - pi (3.5/2)^2   = about  54.38 in^2

\(\text{Area of square cloth}=8^2 \space \text{sq. in.}=64\space\text{sq. in.}\)

\(\text{Area of the circle hole :P = }\pi \times(\frac{7}{4})^2=\frac{49\pi}{16}\space\text{sq. in.}\)

\(\text{Area that remains}= 64 - \frac{49\pi}{16}\approx 54.3788725\)