Question

the radius of the Outer Circle is 2x cm and the radius of the inside circle is 6 cm the area of the Shaded region is 288 Pi centimeters squared. What is the value of x

Answer 1

For this case we have that by definition, the area of a circle is given by:

$A = \pi * r ^ 2$

Where:

r: It is the radius of the circle.

So, we have that the area of the shaded region is given by:

$\pi * (2x) ^ 2- \pi * 6 ^ 2 = 288 \pi\\4x ^ 2-36 = 288\\4x ^ 2 = 288 + 36\\4x ^ 2 = 324$

We divide between 4 on both sides of the equation:

$x ^ 2 = 81$

We apply root to both sides:

$x = \pm \sqrt {81}$

We choose the positive value of the root:

$x = \sqrt {81}\\x = 9$

Finally, the value of "x" is 9

Answer:

$x = 9$