III gimnazjum

Matematyka z plusem 3

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/29071/4CY51I08Q5UXLqGG0SI3RQ%3D%3D_2cbe4ea0007b92a6422ea89aae9152eae6062b18335a10af9350beb1764634fc.jpg" width="358" height="330"> α=180o−2⋅40o=180o−80o=100o <section class="answer"><h4 class="answer-heading">Odpowiedź:</h4> C</section>

Rozwiązanie 1

Promień walca będzie miał długość 6, natomiast jego wysokość będzie mieć długość 4.

Objętość świeczki pozostaje taka sama, więc:    π⋅(4:2)2⋅10=π⋅(2:2)2⋅h

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/29072/vFWeTfPh4vzym6n0Qil9Xw%3D%3D_05bc8565bcb39fbd7b3def92473b39eb988efbb1356d035cc88057242707d236.jpg"> 2b=10   ⇒   b=10:2=5   ⇒   b3<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
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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>​=53<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
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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>​

Vwalca​=πr2⋅h

31​⋅π⋅r2⋅10=120   ∣:10

Tworząca stożka ma długość 4. Obliczamy pole boczne na 2 sposoby (jako  43​

Przed zmianą:  d1​=38 mm r1​=38 mm:2=19 mm

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