Answer:
Volume of the cone is approximately 0.8 cubic meters
Step-by-step explanation:
Recall that the volume of a circular cone is defined by:
[tex]V=\pi R^2\,\frac{H}{3}[/tex]
where R is the radius of the cone's base, and H the cone's height. Since we have the information of the height H (5.7 m) we just need to find the radius R. We can do such by using the other piece of information: the circumference of its base.
The circumference of a circle is the product: [tex]2\,\pi\,R[/tex]
So by knowing the circumference's length (2.3 m) we can solve for the radius R:
[tex]2.3\,m=2\,\pi\,R\\R=\frac{2.3}{2\,\pi} \,m\\R=0.366\,m[/tex]
We can now use this result in the formula for the volume:
[tex]V=\pi ^2\,\frac{H}{3}\\V=\pi (0.366)^2\,\frac{5.7}{3}\,m^3\\V=0.7995868\, m^3[/tex]which can be rounded to the nearest tenth as:
[tex]V=0.8\,m^3[/tex]
