Given:
Given that the radius of the cone is 3 units.
The volume of the cone is 57 cubic units.
We need to determine the height of the cone.
Height of the cone:
The height of the cone can be determined using the formula,
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
Substituting the values, r = 3 and V = 57, we get;
[tex]57=\frac{1}{3} (3.14) (3)^2 h[/tex]
Simplifying the terms, we get;
[tex]57=\frac{1}{3} (3.14) (9) h[/tex]
Multiplying both sides of the equation by 3, we get;
[tex]171= (3.14) (9) h[/tex]
[tex]171=28.26 h[/tex]
Dividing both sides of the equation by 28.26, we get;
[tex]6.05=h[/tex]
Thus, the height of the cone is 6.05 units.
