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