3. the radius of the entire dartboard is 40 cm, while the radius of the red circle is 20 cm. if a dart is…

3. the radius of the entire dartboard is 40 cm, while the radius of the red circle is 20 cm. if a dart is thrown at random, find the probability that it will land in the red circle. justify your answer. hint: divide the area of the red circle by the area of the dartboard.

3. the radius of the entire dartboard is 40 cm, while the radius of the red circle is 20 cm. if a dart is thrown at random, find the probability that it will land in the red circle. justify your answer. hint: divide the area of the red circle by the area of the dartboard.

Answer

Explanation:

Step1: Find area of red - circle

The formula for the area of a circle is $A = \pi r^{2}$. For the red - circle with radius $r_1=20$ cm, its area $A_1=\pi r_1^{2}=\pi\times(20)^{2}=400\pi$ $cm^{2}$.

Step2: Find area of dart - board

For the dart - board with radius $r_2 = 40$ cm, its area $A_2=\pi r_2^{2}=\pi\times(40)^{2}=1600\pi$ $cm^{2}$.

Step3: Calculate probability

The probability $P$ that the dart lands in the red circle is given by the ratio of the area of the red circle to the area of the dart - board. So $P=\frac{A_1}{A_2}=\frac{400\pi}{1600\pi}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$