Question

a dartboard consists of a circle inscribed in a square. the area of the circle is 25π square units. the area of the square is 100 square units. megan randomly throws a dart at the square. assuming the dart lands within the square, what is the probability that the dart lands within the dartboard? round your answer to the nearest tenth of a percent.

Explanation:

Step1: Recall probability formula

The probability $P$ of an event is given by $P=\frac{\text{Favorable Area}}{\text{Total Area}}$.

Step2: Identify favorable and total areas

The favorable area (area of the circle - the dartboard) is $A_{circle}=25\pi$ square units, and the total area (area of the square) is $A_{square} = 100$ square units.

Step3: Calculate the probability

$P=\frac{25\pi}{100}=\frac{\pi}{4}$.

Step4: Convert to percentage

$P=\frac{\pi}{4}\times100\% = 25\pi\%$. Substituting $\pi\approx3.14159$, we get $P\approx 78.5\%$.

Answer:

$78.5\%$