Zadanie 1 0,12 π mm: 2πr = 0,12π mm /:π 2r = 0,12 /:2 r = 0,06 P = πr² P = π(0,06)² P = 0,0036π mm² ================================ ⅔ π km: 2πr = ⅔π km /:π 2r = 2/3 /:2 r = 1/3 P = πr² P = 1/9π km² ================================ 4dm: 2πr = 4dm /:2 πr = 2 /:π r = 2/π P = πr² P = π(2/π)² P = 4/π dm² =================================== Zadanie 2 4/9πm²: πr² = ⁴/₉π m² /:π r² = 4/9 r = 2/3 Obw = 2πr Obw = 2 * π * 2/3 Obw = 4/3π m ============================== πr² = 0,25π mm² /:π r² = 0,25 r = 0,5 Obw = 2πr Obw = 2 * π * 0,5 Obw = π mm ============================= πr² = 2π dm² /:π r² = 2 r = √2 Obw = 2πr Obw = 2 * π * √2 Obw = 2√2π dm
[latex]O = 2 pi r[/latex] [latex]P = pi r^2[/latex] 1a) [latex]O = 0,12 pi mm[/latex] [latex]2 pi r = 0,12 pi / : 2 pi[/latex] [latex]r = 0,06 mm[/latex] [latex]P = pi (0,06)^2 = 0,0036 pi mm^2[/latex] 1b) [latex]O = frac{2}{3} pi km[/latex] [latex]2 pi r = frac{2}{3} pi / : 2 pi [/latex] [latex]r = frac{1}{3} km[/latex] [latex]P = pi (frac{1}{3})^2 = frac{1}{9} pi km^2 [/latex] 1c) [latex]O = 4 dm[/latex] [latex]2 pi r = 4 / : 2 pi [/latex] [latex]r = frac{2}{pi} dm[/latex] [latex]P = pi (frac{2}{pi})^2 = frac{4}{pi^2} cdot pi = frac{4}{pi} dm^2 [/latex] 2a) [latex]P = frac{4}{9} pi m^2[/latex] [latex]pi r^2 = frac{4}{9} pi / : pi[/latex] [latex]r^2 = frac{4}{9}[/latex] [latex]r = sqrt{frac{4}{9}} = frac{2}{3} m[/latex] [latex]O = 2 pi cdot frac{2}{3} = frac{4}{3} pi m[/latex] 2b) [latex]P = 0,25 pi = frac{25}{100} pi mm^2[/latex] [latex]pi r^2 =frac{25}{100} pi / : pi[/latex] [latex]r^2 = frac{25}{100}[/latex] [latex]r = sqrt{frac{25}{100}} = frac{5}{10} = frac{1}{2} mm[/latex] [latex]O = 2 pi cdot frac{1}{2} = pi mm [/latex] 2c) [latex]P = 2 pi dm^2[/latex] [latex]pi r^2 = 2pi / : pi[/latex] [latex]r^2 = 2[/latex] [latex]r = sqrt{2} dm[/latex] [latex]O = 2 pi sqrt{2} = 2sqrt {2} pi dm [/latex]
