Answer:
The volume of a cone is calculated using the formula below
[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]
The height is multiplied by 4, we will have the new height be
[tex]\begin{gathered} h=4\times h \\ h=4h \end{gathered}[/tex]
The radius id multiplied by 4, we will have the new radius be
[tex]\begin{gathered} r=4\times r \\ r=4r \end{gathered}[/tex]
By substituting the new values of the height and radius in the equation od the volume of a cone, we will have
[tex]\begin{gathered} V_{cone}=\frac{1}{3}\times\pi r^2h \\ V_2=\frac{1}{3}\times\pi\times(4r)^2\times(4h) \\ V_1=\frac{1}{3}\times64\pi r^2h \\ V_1=\frac{64}{3}\pi r^2h \end{gathered}[/tex]
By dividing the new volume by the initial volume, we will have
[tex]\begin{gathered} =\frac{\frac{64}{3}\pi r^2h}{\frac{1}{3}\pi r^2h} \\ =64 \end{gathered}[/tex]
Hence,
The final answer is
The volume of the cone is multiplied by 64
