The expression for the volume of cone is :
[tex]\begin{gathered} \text{Volume of Cone =}\frac{1}{3}\Pi r^2h \\ \text{where r = radius, h =height} \end{gathered}[/tex]
Since from the given figure we have, height of cone h= 12 mm
and from the given data, volum is V = 1519.76 cubic milimeter.
Subtitute the values in the expression for the volume of cone and solve for radius r,
[tex]\begin{gathered} V=\frac{1}{3}\Pi r^2h \\ 1519.76=\frac{1}{3}\Pi r^2(12) \\ \text{ since, }\Pi=3.14 \\ \frac{1519.76\times3}{\Pi(12)}=r^2 \\ r^2=\frac{4559.28}{37.68} \\ r^2=121 \\ r=\sqrt[]{121} \\ r=11\text{ mm} \end{gathered}[/tex]
So, the radius of cone is 11 mm.
Answer : 11 mm
