Answer:
The volume of the new cone would be;
[tex]469\text{ cubic centimeter}[/tex]Explanation:
Given the cone in the attached image.
with radius r and height h of;
[tex]\begin{gathered} r=4\operatorname{cm} \\ h=5\operatorname{cm} \end{gathered}[/tex]If the radius was doubled and the height changed to 7cm, we would have;
[tex]\begin{gathered} r_1=2(4\operatorname{cm})=8\operatorname{cm} \\ h_1=7\operatorname{cm} \end{gathered}[/tex]The Volume of a cone can be calculated using the formula;
[tex]V=\frac{1}{3}\pi r^2h[/tex]substituting the new radius and height;
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2_1h_1 \\ V=\frac{1}{3}\pi(8^2)(7) \\ V=469.14 \\ V=469\text{ cubic centimeter} \end{gathered}[/tex]Therefore, the volume of the new cone would be;
[tex]469\text{ cubic centimeter}[/tex]