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?
α−the angle of a sliceR−radiusPerimeter:90=2R+αR⇒α=90R−2Area:S=α2R2=(45R−1)R2=45R−R245R−R2→maxRmax=−452⋅(−1)=22.5Diameter:d=2R=45\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\\α−theangleofasliceR−radiusPerimeter:90=2R+αR⇒α=R90−2Area:S=2αR2=(R45−1)R2=45R−R245R−R2→maxRmax=2⋅(−1)−45=22.5Diameter:d=2R=45
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