[tex]r_{1} = x\\P_{1} = \pi r^{2} = \pi x^{2}[/tex]
[tex]r_{2} = \frac{x}{4} \\P_{2} = \pi r^{2} = \pi (\frac{x}{4})^{2} = \pi \frac{x^{2}}{16} \\[/tex]
[tex]\frac{P_{1}}{P_{2}} = \frac{\pi x^{2}}{\frac{x^{2}}{16}\pi } = \frac{x^{2}}{\frac{x^{2}}{16} } = x^{2} * \frac{16}{x^{2}} = 16\\\\\frac{P_{1}}{P_{2}} = 16\\\\P_{1} = P_{2}*16[/tex]
Odp: Po zmiejszeniu promienia 4 razy, pole koła maleje 16 razy.
