calcule a área a base e a a área lateral de um cone reto de 6cm de altura e 10cm de geratriz ? Por Farvor
Respostas
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Boa noite Larissa!
Solução!
Vamos determinar o raio da base do cono!
![G=10cm\\\\\\
H=6cm\\\\\
(10)^{2}=(6)^{2} +R^{2}\\\\\\
100=36+R^{2}\\\\\\
100-36=R^{2}\\\\\\
64=R^{2}\\\\\
R= \sqrt{64}\\\\\
\boxed{Raio=8cm}](https://tex.z-dn.net/?f=G%3D10cm%5C%5C%5C%5C%5C%5C%0AH%3D6cm%5C%5C%5C%5C%5C%0A%0A%2810%29%5E%7B2%7D%3D%286%29%5E%7B2%7D+%2BR%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A100%3D36%2BR%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A100-36%3DR%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A64%3DR%5E%7B2%7D%5C%5C%5C%5C%5C%0AR%3D+%5Csqrt%7B64%7D%5C%5C%5C%5C%5C%0A%5Cboxed%7BRaio%3D8cm%7D++++++ "G=10cm\\\\\\
H=6cm\\\\\
(10)^{2}=(6)^{2} +R^{2}\\\\\\
100=36+R^{2}\\\\\\
100-36=R^{2}\\\\\\
64=R^{2}\\\\\
R= \sqrt{64}\\\\\
\boxed{Raio=8cm}")
Vamos agora calcular a área da base!
![Area_{(base)}= \pi \times R^{2}\\\\\\
Area_{(base)}= \pi \times (8)^{2}\\\\\\
\boxed{Area_{(base)}= 64 \pi cm^{2} } \\\\\\
Ou\\\\\
Area_{(base)}= 64 \times3,14 \\\\\\
\boxed{Area_{(base)}=200,96cm^{2}}](https://tex.z-dn.net/?f=Area_%7B%28base%29%7D%3D+%5Cpi+%5Ctimes+R%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A+Area_%7B%28base%29%7D%3D+%5Cpi+%5Ctimes+%288%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A+%5Cboxed%7BArea_%7B%28base%29%7D%3D+64+%5Cpi+cm%5E%7B2%7D+%7D+%5C%5C%5C%5C%5C%5C%0AOu%5C%5C%5C%5C%5C%0AArea_%7B%28base%29%7D%3D+64+%5Ctimes3%2C14+%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BArea_%7B%28base%29%7D%3D200%2C96cm%5E%7B2%7D%7D+ "Area_{(base)}= \pi \times R^{2}\\\\\\
Area_{(base)}= \pi \times (8)^{2}\\\\\\
\boxed{Area_{(base)}= 64 \pi cm^{2} } \\\\\\
Ou\\\\\
Area_{(base)}= 64 \times3,14 \\\\\\
\boxed{Area_{(base)}=200,96cm^{2}}")
Lembrando que a área lateral corresponde à área de um setor circular.
![Area _{(lateral)}= \pi \times R\times G\\\\\\\
Area _{(lateral)}= \pi \times 8 \times 10\\\\\\\
\boxed{Area _{(lateral)}= 80 \pi cm^{2} } \\\\\\\
Ou\\\\\\
Area _{(lateral)}= 80\times 3,14 \\\\\\\
\boxed{Area _{(lateral)}= 251,2 cm^{2} }](https://tex.z-dn.net/?f=Area+_%7B%28lateral%29%7D%3D+%5Cpi+%5Ctimes+R%5Ctimes+G%5C%5C%5C%5C%5C%5C%5C%0A+Area+_%7B%28lateral%29%7D%3D+%5Cpi+%5Ctimes+8+%5Ctimes+10%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BArea+_%7B%28lateral%29%7D%3D+80+%5Cpi+cm%5E%7B2%7D+%7D+%5C%5C%5C%5C%5C%5C%5C%0AOu%5C%5C%5C%5C%5C%5C%0AArea+_%7B%28lateral%29%7D%3D+80%5Ctimes+3%2C14+%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BArea+_%7B%28lateral%29%7D%3D+251%2C2+cm%5E%7B2%7D+%7D+ "Area _{(lateral)}= \pi \times R\times G\\\\\\\
Area _{(lateral)}= \pi \times 8 \times 10\\\\\\\
\boxed{Area _{(lateral)}= 80 \pi cm^{2} } \\\\\\\
Ou\\\\\\
Area _{(lateral)}= 80\times 3,14 \\\\\\\
\boxed{Area _{(lateral)}= 251,2 cm^{2} }")
Boa noite!
Bons estudos!
Solução!
Vamos determinar o raio da base do cono!
Vamos agora calcular a área da base!
Lembrando que a área lateral corresponde à área de um setor circular.
Boa noite!
Bons estudos!
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