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 $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. In terms of area, if we want to find the probability that the dart lands in the circle (dart - board) within the square, $P = \frac{\text{Area of the circle}}{\text{Area of the square}}$.

Step2: Substitute given values

We are given that the area of the circle $A_{circle}=25\pi$ square units and the area of the square $A_{square} = 100$ square units. So, $P=\frac{25\pi}{100}$.

Step3: Calculate the value of the fraction

First, simplify $\frac{25\pi}{100}=\frac{\pi}{4}$. Then, $\frac{\pi}{4}\approx\frac{3.14159}{4}=0.7853975$.

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100. So, $0.7853975\times100 = 78.53975\%$.

Step5: Round to the nearest tenth of a percent

Rounding $78.53975\%$ to the nearest tenth of a percent gives $78.5\%$.

Answer:

$78.5\%$