III gimnazjum

Matematyka wokół nas 3

a) 82+62<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
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c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
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c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z'/></svg>​=64+36<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​=100<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​=10

h=32<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ cm &nbsp; r=3 cm

r=3331​%⋅18cm=300100​⋅18cm=6cm

Przez obrót &nbsp;trójkąta prostokątnego o bokach długości a, b oraz c (a≤b&lt;c) można otrzymać stożek na dwa sposoby: Sposób I: obracamy trójkąt wokół przyprostokątnej a <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24154/VJ/AkLPLHX/MMbMCiEljRA%3D%3D_b832d3dcda2747cc02d63cdc24239752861279e6326998022d889521d4663f32.jpg" width="397" height="356"> Określamy promień podstawy (r) oraz wysokość stożka (h): r=b h=a

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24161/QUdihlO0UoZBcHGB8bENcQ%3D%3D_7666d724ce2773077026c9eabbb0a1dca118fa74bdf732f9d74abe9197fccec7.jpg" width="445" height="480"> ∣∠ACB∣=30o l = 2r 242+r2=l2

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/24170/A4o%2BuRbAmTejpS2zgcwlIw%3D%3D_6170cb900f169511107060c255081476c5b9178b0dc5183979c6ffa62f664090.jpg" width="483" height="480"> r=21​⋅16cm=8cm

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