Question

a dartboard consists of a circle inscribed in a square. the area of the circle is 16π square inches. the area of the square is 64 square inches. izzy randomly throws a dart at the square, and it lands inside the square. to the nearest percent, what is the probability that the dart lands inside the square but not on the circular dartboard? use 3.14 for π.

Explanation:

Step1: Calculate area outside circle in square

The area of the square is $A_{square}=64$ square - inches and the area of the circle is $A_{circle}=16\pi$ square - inches. Using $\pi = 3.14$, $A_{circle}=16\times3.14 = 50.24$ square - inches. The area of the region inside the square but outside the circle is $A = A_{square}-A_{circle}=64 - 50.24=13.76$ square - inches.

Step2: Calculate the probability

The probability $P$ that the dart lands inside the square but not on the circular dart - board is given by the formula $P=\frac{A}{A_{square}}$. Substituting the values, we get $P=\frac{13.76}{64}=0.215$.

Step3: Convert probability to percentage

To convert the probability to a percentage, we multiply by 100. So $P = 0.215\times100 = 21.5\%\approx22\%$.

Answer:

22%