Question

a circle is inscribed perfectly inside a square with a side - length of 10cm. what is the area of the region that is inside the square but outside the circle?
a. 100 - 10π
b. 100 - 25π
c. 40 - 10π
d. 40 - 25π

Explanation:

Step1: Calculate area of the square

The area formula for a square is $A_{square}=s^2$, where $s = 10$ cm. So $A_{square}=10^2=100$ $cm^2$.

Step2: Calculate radius of the circle

Since the circle is inscribed in the square, the diameter of the circle is equal to the side - length of the square. So the diameter $d = 10$ cm, and the radius $r=\frac{d}{2}=5$ cm.

Step3: Calculate area of the circle

The area formula for a circle is $A_{circle}=\pi r^2$. Substituting $r = 5$ cm, we get $A_{circle}=\pi\times5^2 = 25\pi$ $cm^2$.

Step4: Calculate the required area

The area of the region inside the square but outside the circle is $A=A_{square}-A_{circle}=100 - 25\pi$ $cm^2$.

Answer:

B. $100 - 25\pi$