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aFind the probability that a randomlyselected point within the circle fallsin the white area.r= 4 cm[? ]%Round to the nearest tenth of a nercent

AFind The Probability That A Randomlyselected Point Within The Circle Fallsin The White Arear 4 Cm Round To The Nearest Tenth Of A Nercent class=

Sagot :

In order to find the probability, first we need to calculate the triangle area and the circle area.

The triangle has a base of 8 cm and a height of 4 cm, so its area is:

[tex]A_t=\frac{8\cdot4}{2}=4\cdot4=16\text{ cm}^2[/tex]

The circle has a radius of 4 cm, so:

[tex]A_c=\pi r^2=3.1416\cdot4^2=50.2656[/tex]

Now, to find the probability, we divide the white area (circle minus triangle) by the total area (circle):

[tex]P=\frac{A_c-A_t}{A_c}=\frac{50.2656-16}{50.2656}=\frac{34.2656}{50.2656}=0.68169[/tex]

Rounding to the nearest tenth of a percent, we have a probability of 68.2%.

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