Question

Can anyone please help me this? stuck with this problem for hours

Answer 1

Answer:

p = 18.24 cm²

chance = 36.30%

Step-by-step explanation:

To solve this, you must find the area of both the square and the circle. Note that:

- one side of the square is 4√2 cm long.

- the radius of the circle is 4 cm long.

First, know the equation in how to solve for each area:

Area of Square: A = s² = side x side

Next, know the equation for the circle:

Area of Circle: A = πr²

plug in the corresponding numbers to the corresponding variables:

Area of square:

A = s²

s = 4√2

A = (4√2)² = 4√2 * 4√2 = 4 * 4 * √2 * √2  = 16 * 2 = 32

Your area of the square is 32 cm²

Area of circle:

A = πr²

r = 4

A = π(4)² = π(4 * 4) = π(16) = (3.14)(16) = 50.24

Your area of the circle is 50.24 cm²

Solve for the probability of the point landing in the white area by subtracting the total area of the circle with the area of the square:

50.24 - 32 = 18.24 cm²

p = 18.24 cm²

Now, to get the percentile chance of landing in the white area, divide the number gotten from total area:

18.24/50.24 = 0.3630 = 36.30%

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Answer 2

First time the area of the circle and the square.
The radius of the first is 4, so the area of the circle is 16pi.
The area of the square is 32.
You can subtract the area of the circle by the square because some most of the circle is being covered by the square.
16pi-32 is the area of the circle that is visible.
16pi-32:32 can be simplified to pi-2:2
So the probability that a randomly selected point within the circle falls in the white area is
pi-2:2 or in decimal terms, ≈1.14:2