Answer:
8 meters
Step-by-step explanation:
To find the radius of a cone given its volume, we can use the volume of a cone formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cone}}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
In this case:
- V = 1607.68 m³
- h = 24 m
- π = 3.14
Substitute the values into the formula and solve for r:
[tex]\dfrac{1}{3}\cdot 3.14\cdot r^2\cdot 24=1607.68\\\\\\\dfrac{1}{3}\cdot 75.36\cdot r^2=1607.68\\\\\\25.12r^2=1607.68\\\\\\r^2=\dfrac{1607.68}{25.12}\\\\\\r^2=64\\\\\\r=\sqrt{64}\\\\\\r=8[/tex]
Therefore, the radius of the given cone is:
[tex]\LARGE\boxed{\boxed{r\approx8\; \sf meters}}[/tex]
