Pizza

Pizza with a diameter of 40 cm weights 409 g. What diameter will a pizza weigh 764 g made from the same cloth (same thickness) and decorated?

Final Answer:

d₂ =  54.7 cm

Step-by-step explanation:

$$\begin{gathered} d_1=40\text{cm} \\ {m}_1=409\text{g} \\ {m}_2=764\text{g} \\ {m}_1=\rho S_1 \\ {r}_1=d_1/2=40/2=20\text{cm} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 20^2\doteq 1256.6371{\text{cm}}^2 \\ \rho =m_1/S_1=409/1256.6371\doteq 0.3255{\text{g/cm}}^2 \\ \rho =m_2/S_2 \\ {S}_2=m_2/\rho =764/0.3255\doteq 2347.3612{\text{cm}}^2 \\ {S}_2=\pi r_2^2 \\ {r}_2=\sqrt{S_2/\pi }=\sqrt{2347.3612/3.1416}\doteq 27.3347\text{cm} \\ {d}_2=2\cdot r_2=2\cdot 27.3347=54.7\text{cm} \end{gathered}$$

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