the radii of three concentric circles shown are in the ratio 1:2:3. What is the probability that random shot that hits the target will hit inside the second circle but inside the innermost circle?
11:3
To calculate the probability, we need to determine the ratio of the areas of the second circle and the innermost circle.
Let's assume the radius of the innermost circle is "x." Therefore, the radius of the second circle would be "2x" (since their ratios are 1:2).
The formula to calculate the area of a circle is A = π * r^2, where "A" is the area and "r" is the radius.
Let's calculate the areas of the two circles.
Area of the innermost circle = π * x^2
Area of the second circle = π * (2x)^2 = π * 4x^2 = 4π * x^2
Now we can determine the probability that a random shot will hit inside the second circle but inside the innermost circle, which is the ratio between the areas of the two circles:
Probability = Area of the second circle / Area of the innermost circle
Probability = (4π * x^2) / (π * x^2)
Probability = 4
Therefore, the probability that a random shot will hit inside the second circle but inside the innermost circle is 4.