Question

show full work! or drawing a diagram would be helpful!

Answer 1

We first determine which aperture (angle) is in degrees:

*First angle:

$\frac{\pi}{3}\cdot\frac{180}{\pi}=60$

*Second angle:

$\frac{\pi}{4}\cdot\frac{180}{\pi}=45$

Now, we determine the areas of each pizza slice:

*First slice:

$A_1=\pi(7)^2(\frac{60}{360})\Rightarrow A_1=\frac{49}{6}\pi\Rightarrow A_1\approx25.7$

*Second slice:

$A_2=\pi(8)^2(\frac{45}{360})\Rightarrow A_2=8\pi\Rightarrow A_2\approx25.1$

From this, we can see that it would be a better deal to buy the slice of the 14-inch pizza.