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[latex]4.\r = 4 cm\P_{p osiowego} = 40 cm^{2}\P_{c} = ?\\P_{p} = 2rcdot H /:2r\\H = frac{P_{p}}{2r} =frac{40cm^{2}}{2cdot4cm} = 5 cm\\P_{c} = 2 pi r^{2}+2 pi rH = 2 pi r(r+H)\\P_{c} = 2 pi cdot4cmcdot(4cm+5cm) = 8 pi cmcdot9cm = 72 pi cm^{2}[/latex] [latex]5.\d = 12 cm\H - wys. walca\r - promien walca\\a)\alpha = 30^{o}\sin30^{o} = frac{1}{2}\cos60^{o} = frac{sqrt{3}}{2}\\frac{H}{d} = sinalpha\H = dcdot sinalpha=12cdotfrac{1}{2} = 6 cm\\frac{2r}{d} = cosalpha\2r = dcdot cosalpha = 12cdotfrac{sqrt{3}}{2} = 6sqrt{3} cm\r = 3sqrt{3} cm\\P_{c} = 2 pi (r^{2}+rH)\\P_{c} = 2 pi cdot((3sqrt{3})^{2}+3sqrt{3}cdot6) = 2 pi cdot27+18sqrt{3} = 18 pi (3+2sqrt{3}) cm^{2} [/latex] [latex]b)\d = 12 cm\alpha = 45^{o}\P_{c} = ?\\Z tw. Pitagorasa:\H^{2}+H^{2} = d^{2}\2H^{2} = 12^{2}\2H^{2} = 144 /:2\H^2} = 72\H = sqrt{72} = sqrt{36cdot2}=6sqrt{2} cm\\2r = H /:2\r = frac{1}{2}H=frac{1}{2}cdot6sqrt{2} = 3sqrt{2} cm\\P_{c} = 2 pi (r^{2}+rH) \\P_{c} = 2 pi ((3sqrt{2})^{2}+3sqrt{2}cdot6sqrt{2})) = 2 pi (18+36) = 2 pi cdot54=108 pi cm^{2}[/latex]
