dwie kulki o pronieniach 3 cm i 6 cm przetopiono i odlano w jedna kulke wyznacz ppc i r tej kuli

[latex]V_1 - obj. pierwszej kuli\V_1 = 4/3pi r^3 \r = 3 cm\V_1 = 4/3*pi*3^3 = 4/3*27*pi = 36pi cm^3\V_2 = 4/3pi R^3\R = 6 cm\V_2 - obj. drugiej\V_2 = 4/3*pi*6^3 = 288pi cm^3\\V - obj. nowej kuli\V = V_1+V_2\V = 36pi+288pi = 324pi cm^3\R = ?\324pi = 4/3pi*R^3 |:pi\324 = 4/3R^3 |*3/4\R^3 =243 \old{R = sqrt[3]{243} = sqrt[3]{3^5} = 3sqrt[3]9} cm\\old{Pc} = 4pi R^2 = 4pi*(3sqrt[3]9)^2 = 4pi*9*sqrt[3]{3^4} = 36*3*sqrt[3]3*pi =\= old{108sqrt[3]3pi cm^2}[/latex]