Answer:
15 units
Step-by-step explanation:
The formula for the volume of a cone is:
V = [tex]\frac{\pi r^{2}h }{3}[/tex]
Where V is the volume, r is the radius, and h is the height
Substitute:
90 = [tex]\frac{18h }{3}[/tex]
Since the base of a cone is a circle, the base area is [tex]\pi r^{2}[/tex]. This means that 18 can be substituted in the formula for [tex]\pi r^{2}[/tex].
Solve:
90 = [tex]\frac{18h }{3}[/tex]
Multiply by 3 on both sides:
90 = [tex]\frac{18h }{3}[/tex]
3(90) = ([tex]\frac{18h }{3}[/tex])3
270 = 18h
Divide by 18 on both sides:
270 = 18h
/18 /18
15 ≈ h
Therefore, the height of the cone is 15 units.
