Question

find the probability that a randomly selected point within the circle falls in the red shaded area round to the nearest hundredth r = 4 cm 2.5 cm 3 cm 3 cm

Answer 1

`p\approx 0.39`

Explanation:

We are given a circle of radius 4 cm, and a triangle inscribed within the circle with a vertical height of 6.5 cm and a base of 6 cm.

To find the probability a randomly selected point lands in the red area, we can divide the red area by the total area.

The area for a circle is given by:

`A=\pi r^2`

Since the radius is 4 cm, the area of the circle or total area is:

`A=\pi (4)^2=16\pi \text{ cm}^2`

The area for a triangle is given by:

`\displaystyle A=(1)/(2)bh`

The base of the triangle is 6 cm total and the vertical height is 6.5 cm. Therefore, the area is:

`\displaystyle A=(1)/(2)(6)(6.5)=19.5\text{ cm}^2`

The probability of landing in the red shaded area is:

`\displaystyle p=\frac{\text{Red Region}}{\text{Total Region}}`

Therefore:

`\displaystyle p=(19.5)/(16\pi)\approx 0.39=39\%`