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The circumference of a circle is 28. Contained in that circle is a smaller circle with area 36π. A point is selected at random from inside the large circle. What is the probability the point also lies in the smaller circle?

Sagot :

Answer:

[tex]Pr = \frac{9}{49}[/tex]

Step-by-step explanation:

Given

[tex]d = 28[/tex] --- big circle

[tex]A_2 = 36 \pi[/tex] --- area of small circle

Required

Probability that a point selected lands on the small circle

Calculate the area of the big circle using;

[tex]A_1 = \pi r^2[/tex]

Where

[tex]r = d/2[/tex]

So, we have:

[tex]r = 28/2 = 14[/tex]

This gives:

[tex]A_1 = \pi * 14^2[/tex]

[tex]A_1 = \pi * 196[/tex]

[tex]A_1 = 196\pi[/tex]

The probability that a point selected lands on the small circle is calculated by dividing the area of the small cicle by the big circle

This gives:

[tex]Pr = \frac{36\pi}{196\pi}[/tex]

[tex]Pr = \frac{36}{196}[/tex]

Simplify

[tex]Pr = \frac{9}{49}[/tex]