Question

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?

Answer 1

Answer:

$Pr = \frac{9}{49}$

Step-by-step explanation:

Given

$d = 28$ --- big circle

$A_2 = 36 \pi$ --- area of small circle

Required

Probability that a point selected lands on the small circle

Calculate the area of the big circle using;

$A_1 = \pi r^2$

Where

$r = d/2$

So, we have:

$r = 28/2 = 14$

This gives:

$A_1 = \pi * 14^2$

$A_1 = \pi * 196$

$A_1 = 196\pi$

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:

$Pr = \frac{36\pi}{196\pi}$

$Pr = \frac{36}{196}$

Simplify

$Pr = \frac{9}{49}$