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ANSWER
[tex]V=7179.09\operatorname{mm}[/tex]EXPLANATION
We are given the height of the cone as 19 mm and the diameter of its base as 38 mm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}\pi\cdot r^2h[/tex]where r =radius; h = height
The diameter of a circle (the base of a cone) is twice the radius. Therefore:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{38}{2} \\ r=19\operatorname{mm} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot19^2\cdot19 \\ V=7179.09\operatorname{mm}^3 \end{gathered}[/tex]
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