Odpowiedź:
1. P = 1/2πr^2 = 16π * 1/2 = 8π, P2 = πr2^2
8π = πr2^2 | : π
8 = r2^2
r2 = pierwiastek z 8 = 2 pierwiastki z 2 odp d
2. kąt oznacze jako S
S = 360 * P/πr^2
S = 360 * π/8πr^2
S = 360 * 1/8r^2
S = 360 * 1/72 = 5 stopni
Szczegółowe wyjaśnienie:
T1.
[tex]r = 4\\\\P = \pi r^{2} = \pi\cdot4^{2} = 16\pi\\\\\frac{1}{2}P=\frac{1}{2}\cdot16\pi\\\\\underline{\frac{1}{2}P = 8\pi}[/tex]
[tex]A. \ dla \ r = 1\\\\P = \pi r^{2}=\pi \cdot1^{2} = \pi \neq 8\pi[/tex]
[tex]B. \ dla \ r = 2\\\\P = \pi r^{2} = \pi \cdot2^{2} = 4\pi \neq 8\pi[/tex]
[tex]C. \ dla \ r = \sqrt{2}\\\\P = \pi r^{2} = \pi \cdot\sqrt{2}^{2} = 2\pi \neq 8\pi[/tex]
[tex]\underline{D. \ dla \ r = 2\sqrt{2}}\\\\P = \pi r^{2} = \pi \cdot(2\sqrt{2})^{2} =\boxed{ 8\pi}[/tex]
[tex]\boxed{Odp. \ D}[/tex]
T2.
[tex]r = 3 \ cm\\P_{w} = \frac{\pi}{8}\\\alpha = ?[/tex]
Korzystamy ze wzoru na pole wycinka koła:
[tex]P_{w} = \frac{\alpha}{360^{o}}\cdot \pi r^{2}\\\\\frac{\pi}{8} = \frac{\alpha}{360^{o}}\cdot \pi \cdot3^{2}\\\\\frac{\pi}{8} = \frac{\alpha \cdot9\pi}{360^{o}}\\\\8\cdot \alpha\cdot9 \pi = 360^{o}\cdot \pi\\\\72\alpha \pi = 360^{o} \pi \ \ \ |:72\pi\\\\\boxed{\alpha = 5^{o}}\\\\\underline{Odp. \ B.}[/tex]
