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50 m³  

(1/3)³ = (0.037037037)*(1350) = 50

Answer: The answer is 2965950 m³.


Step-by-step explanation:  Given that the volume of a cone is 1350 m³. We need to find the volume of the resulting cone when the original cone is dilated by a scale factor of 13.

We know that the volume of a cone with radius of the base 'r' and height 'h' is given by

\(V_o=\dfrac{1}{3}\pi r^2h=1350~\textup{m}^3.\)

After dilation, both the radius and height will be increased by 13 times, so the new volume of the resulting cone will be

\(V_r=\dfrac{1}{3}\pi(13r)^2(13h)\\\\\Rightarrow V_r=13^3\times \dfrac{1}{3}\pi r^2h\\\\\Rightarrow V_r=13^3\times V_o\\\\\Rightarrow V_r=2197\times 1350\\\\\Rightarrow V_r=2965950.\)

Thus, the volume of the resulting cone is 2965950 m³.


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