Pizza

Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?

Correct result:

D =  61.8 cm

Solution:

$m_1 = \rho V_1 = \rho S_1 h \ \\ m_1 = \rho V_1 = \rho S_1 h \ \\ \ \\ \rho = \dfrac{m_1}{S_1 h} = \dfrac{m_2}{S_2 h} \ \\ \ \\ \dfrac{m_1}{S_1} = \dfrac{m_2}{S_2} \ \\ \dfrac{m_1}{ \pi D_1^2/4} = \dfrac{m_2}{ \pi D_2^2/4} \ \\ \dfrac{m_1}{ D_1^2} = \dfrac{m_2}{ D_2^2} \ \\ \ \\ \dfrac{m_1}{ m_2 } = \dfrac{ D_1^2 }{ D_2^2} \ \\ \sqrt{ \dfrac{m_1}{ m_2 } } = \dfrac{ D_1 }{ D_2} \ \\ \ \\ D_2 = D_1 \sqrt{ \dfrac{m_2}{ m_1 } } = 50 \cdot \sqrt{ \dfrac{ 855}{ 559 } } = 61.8 \ \text{cm} \ \\$

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