Answer:
[tex]45m^3[/tex]
Step-by-step explanation:
Volume of cone = 2880 m³
Since the cone is dilated by scale factor of [tex]\frac{1}{4}[/tex]
So, the dimensions will become one-fourth of the previous dimensions
Volume of cone : [tex] 2880=\frac{1}{3} \pi \times r^{2} \times h[/tex] -a
After the dilation by scale factor [tex]\frac{1}{4}[/tex]
[tex]r\rightarrow \frac{r}{4}[/tex]
[tex]h\rightarrow \frac{h}{4}[/tex]
So, [tex]\frac{1}{3} \pi \times\frac{r}{4}^{2} \times\frac{h}{4}[/tex]
[tex]\frac{1}{3} \pi \times\frac{r^2}{16}\times \frac{h}{4}[/tex]
[tex]\frac{1}{64} \times \frac{1}{3} \pi \timesr^2\times h[/tex]
So, the original volume becomes [tex]\frac{1}{64}[/tex]
Using a
[tex]\frac{1}{64} \times2880[/tex]
[tex]45m^3[/tex]
Hence the volume of the resulting cone is [tex]45m^3[/tex]
