Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\boxed{\mathsf{g = 2r}}\leftarrow\textsf{cone equil{\'a}tero}[/tex]

[tex]\mathsf{g^2 = h^2 + r^2}[/tex]

[tex]\mathsf{(2r)^2 = h^2 + r^2}[/tex]

[tex]\mathsf{4r^2 = h^2 + r^2}[/tex]

[tex]\mathsf{h^2 = 3r^2}[/tex]

[tex]\boxed{\mathsf{3g = 36}}\leftarrow\textsf{tri{\^a}ngulo equil{\'a}tero forma a secc{\~a}o meridiana}[/tex]

[tex]\mathsf{g = 12}[/tex]

[tex]\boxed{\boxed{\mathsf{r = 6\:m}}}[/tex]

[tex]\mathsf{h^2 = 3.(6)^2}[/tex]

[tex]\mathsf{h^2 = 3.(36)}[/tex]

[tex]\mathsf{h^2 = 108}[/tex]

[tex]\mathsf{h = 6\sqrt{3}}[/tex]

[tex]\mathsf{h = 6.(1,7)}[/tex]

[tex]\boxed{\boxed{\mathsf{h = 10,2\:m}}}[/tex]

[tex]\mathsf{V = \dfrac{1}{3}\:.\:A_B\:.\:h}[/tex]

[tex]\mathsf{V = \dfrac{1}{3}\:.\:\pi. r^2\:.\:h}[/tex]

[tex]\mathsf{V = \dfrac{1}{\not3}\:.\:\not3. (6)^2\:.\:(10,2)}[/tex]

[tex]\mathsf{V = 36\:.\:(10,2)}[/tex]

[tex]\mathsf{V = 367,2\:m^3}[/tex]

[tex]\boxed{\boxed{\mathsf{V = 367.200\:L}}}[/tex]