Question

If you get a slice of a round pizza with perimeter 90 cm , what should be the diameter of the pizza for you to have gotten the largest slice?

Answer 1

$\alpha -the\,\,angle\,\,of\,\,a\,\,slice\\R-radius\\Perimeter:\\90=2R+\alpha R\Rightarrow \alpha =\frac{90}{R}-2\\Area:\\S=\frac{\alpha}{2}R^2=\left( \frac{45}{R}-1 \right) R^2=45R-R^2\\45R-R^2\rightarrow \max \\R_{\max}=\frac{-45}{2\cdot \left( -1 \right)}=22.5\\Diameter:\\d=2R=45\\$