Odpowiedź:
Twierdzenie Pitagorasa
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {r}^{2} + {h}^{2} = {l}^{2} \\ {4}^{2} + {h}^{2} = {5}^{2} \\ 16 + {h}^{2} = 25 \\ {h}^{2} = 25 - 16 \\ {h}^{2} = 9 \: \: \: \: | \sqrt{} \\ h = 3 \: cm[/tex]
Wzór na objętość stożka
[tex]V \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]V = \frac{1}{3} \times {4}^{2} \times 3 \times \pi = 16\pi \\ V = 16\pi \: {cm}^{3} [/tex]
Wzór na pole stożka
[tex]Pc = Pp + Pb \\ Pp = \pi {r}^{2} \\ Pb = \pi \: \times r \times l[/tex]
[tex]Pp = {4}^{2} \times \pi = 16\pi \\ Pb = 4 \times 5 \times \pi = 20\pi \\ Pc = 16\pi + 20\pi = 36\pi \\ Pc = 36\pi \: {cm}^{2} [/tex]