Answer:
The new volume will be [tex]3\frac{3}{8}[/tex] of its original volume.
Step-by-step explanation:
If the height of a cone is [tex]h[/tex] and the radius is [tex]r[/tex], then its volume is: [tex]\frac{1}{3}\pi r^2 h[/tex]
Now, the height is reduced to [tex]\frac{3}{8}[/tex] of its original length, and its radius is tripled.
That means, the new height [tex]= \frac{3}{8}h[/tex] and the new radius [tex]= 3r[/tex]
So, the new volume will be: [tex]\frac{1}{3}\pi (3r)^2(\frac{3}{8}h) =\frac{1}{3}\pi (9r^2)(\frac{3}{8}h)=\frac{27}{24}\pi r^2h=\frac{9}{8}\pi r^2h[/tex]
Now,
[tex]\frac{\frac{9}{8}\pi r^2h}{\frac{1}{3}\pi r^2 h} \\ \\ =\frac{\frac{9}{8}}{\frac{1}{3}}=\frac{9}{8}\times \frac{3}{1}=\frac{27}{8}=3\frac{3}{8}[/tex]
Thus, the new volume will be [tex]3\frac{3}{8}[/tex] of its original volume.
