The difference between the circumference of circle P and circle Q is 132 cm. If radius of circle Q is 4 times of radius of circle P, then find the area of circle Q (in square cm)?

To find the area of circle Q, we can set up equations based on the relationships given for the radius and the circumference of the two circles.

Let the radius of circle P be $r_P$ and the radius of circle Q be $r_Q$.
We are given that the radius of circle Q is 4 times the radius of circle P:
$r_Q=4r_P$

The circumference of a circle is calculated using the formula:
$C=2\pi r$

We are given that the difference between the circumference of circle Q and circle P is 132 cm:
$2\pi r_Q-2\pi r_P=132$

Substitute the relationship $r_Q=4r_P$ into the equation:
$2\pi \left(4r_P\right)-2\pi r_P=132$
$8\pi r_P-2\pi r_P=132$
$6\pi r_P=132$

Using $\pi =\frac{22}{7}$, we can solve for $r_P$:
$6·\frac{22}{7}·r_P=132$
$\frac{132}{7}·r_P=132$
$r_P=7$ cm

Now, we can find the radius of circle Q ($r_Q$):
$r_Q=4·7=28$ cm

Finally, we calculate the area of circle Q using the formula $A=\pi r^2$:
$A=\frac{22}{7}·28·28$
$A=22·4·28$
$A=88·28=2464$ square cm

Therefore, the correct option is 2464.