Ćwicz. 4
[tex]h = 8 \ cm\\V = 50\pi \ cm^{3}\\r = ?\\\\V = \pi r^{2}h\\\\50\pi = \pi r^{2}\cdot8 \ \ /:2\pi\\\\4r^{2} = 25 \ \ /:4\\\\r^{2} = \frac{25}{4}\\\\r = \sqrt{\frac{25}{4}} = \frac{\sqrt{25}}{\sqrt{4}}= \frac{5}{2} \ cm\\\\\boxed{r = 2,5 \ cm}[/tex]
1.
Walec
[tex]P_{p} = \pi r^{2}\\\\P_{b} = 2\pi rh\\\\P_{c} =2P_{p}+P_{b}\\\\\underline{P_{c} = 2\pi r^{2}+2\pi rh=2\pi r(r+h)}\\\\V = P_{p}\cdot h\\\\\underline{V = \pi r^{2}h}[/tex]
a)
[tex]r = 3,5 \ cm\\h = 4 \ cm\\\\P_{c} = 2\pi r(r+h) = 2\pi\cdot3,5(3,5+4)=7\pi \cdot7,5\\\\\boxed{P_{c} = 52,5\pi \ cm^{2}}\\\\V = \pi r^{2}h = \pi \cdot3,5^{2}\cdot 4=12,25\cdot4\pi\\\\\boxed{V = 49\pi \ cm^{3}}[/tex]
b)
[tex]d = 6 \ cm \ \ \rightarrow \ \ r = 3 \ cm\\h = 8 \ cm\\\\P_{c} = 2\pi r(r+h) = 2\pi \cdot3(3+8)= 6\pi\cdot11\\\\\boxed{P_{c} = 66\pi \ cm^{2}}[/tex]
[tex]V = \pi r^{2}h = \pi \cdot3^{2}\cdot 8 = 9\cdot8 \pi\\\\\boxed{V = 72\pi \ cm^{3}}[/tex]
c)
[tex]r = 4 \ cm\\h = 5 \ cm\\\\P_{c} = 2\pi r(r+h) = 2\pi\cdot4(4+5) = 8\cdot9\pi\\\\\boxed{P_{c} = 72 \ cm^{2}}\\\\V = \pi r^{2}h = \pi \cdot4^{2}\cdot5 = 16\cdot5\pi\\\\\boxed{V = 80\pi \ cm^{3}}[/tex]
