Question

Em um cone reto, a área dá base é 9π cm2 e a geratriz mede √10 cm, calculse o seu volume

Answer 1

Olá FelipeCastrom.



Organizando e resolvendo a equação:

$\mathsf{A_b=r^2\pi}\\\\\mathsf{A_b=9\pi}\\\\\mathsf{r^2\diagup\!\!\!\!\pi=9\diagup\!\!\!\!\pi}\\\\\mathsf{\sqrt{r^2}=\sqrt{9}}\\\\\mathsf{r=3}\\\underline{\qquad\qquad\qquad}\\\\\mathsf{h=altura}\\\\\\\mathsf{h^2+r^2=(\sqrt{10})^2}\\\\\mathsf{h^2+3^2=10}\\\\\mathsf{h^2=10-9}\\\\\mathsf{\sqrt{h}=\sqrt{1}}\\\\\mathsf{h=1}\\\\\underline{\qquad\qquad\qquad}\\\\\\\mathsf{V=r^2\pi\cdot h\cdot\dfrac{1}{3}}\\\\\mathsf{V=\diagup\!\!\!\!9\pi\cdot1\cdot\dfrac{1}{\diagup\!\!\!\!3}}\\\\\\\boxed{\mathsf{V=3\pi~cm^3}}$


Dúvidas? comente.