A 9 inch pizza is in the shape of a circle with a diameter of 9 inches - Junior Cycle Mathematics - Question 14 - 2018

Since the 9 inch pizza is equal to 2 slices of the Big Pizza, the area of one slice of the Big Pizza is: $\text{Area of one Big Pizza slice} = \frac{20.25\pi}{2} = 10.125\pi ext{ square inches}$

Let the radius of the Big Pizza be $R$. Then the area of the Big Pizza is: $A_{big} = \pi R^2$ Since one slice of the Big Pizza has the area $10.125\pi$, and there are 6 slices, we have: $A_{big} = 6 \times 10.125\pi = 60.75\pi$ Thus, we can set up the equation: $\pi R^2 = 60.75\pi$

Cancelling $\pi$ from both sides gives: $R^2 = 60.75$ To find $R$, take the square root: $R = \sqrt{60.75} = \frac{3\sqrt{27}}{2} = \frac{3\sqrt{3 \times 9}}{2} = \frac{3 \times 3 \sqrt{3}}{2} = \frac{9\sqrt{3}}{2}$ Therefore, the radius of the Big Pizza is: $R = \frac{3p}{2}, \text{ where } p = 9\sqrt{3} \in \mathbb{Q}$