Question

A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is 12 in, and the radius of the shaded region is 5 in. Use the value 3.14 for n. Round your answer to the nearest hundredth.

Answer 1

For this problem, we are given the dimensions of a dashboard. We need to determine the probability a dart will hit the shaded area.

To solve this problem, we need to calculate the area of the whole board (square) and the area of the shaded area (circle). Then we need to divide the area of the shaded circle by the entire board.

The area of a circle can be found as shown below:

`A_(shaded)=3.14\cdot(5)^2=78.5\text{ square inches}`

The area of the square can be found as shown below:

`A_(board)=12^2=144\text{ square inches}`

Now we need to find the probability of the shaded area, which can be done by dividing the area of the circle by the area of the board.

`P(shaded)=(78.5)/(144)=0.55`

The probability is 0.55.