Considering the volume of a cone, the height if the cone is 5 units.
A cone is a three-dimensional figure with a circular base, where a curved surface connects the base and the vertex.
The cone is a figure that is generated by rotating a right triangle around one of its legs.
Volume is the place that a body occupies in space.
In the case of the cone, the volume is calculated knowing the height (h) and the radius (r). Its volume is defined as one third of the area of the base B times the height h. This is:
V=[tex]\frac{1}{3}[/tex] ×B ×h
Being B=π× r²
V=[tex]\frac{1}{3}[/tex] ×π× r² ×h
In this case, you know:
- V= 135π units³
- r=diameter÷2= 18 units÷2= 9 units
- h= ?
Replacing:
135π units³= [tex]\frac{1}{3}[/tex]×π× (9 units)² ×h
Solving:
135π units³= [tex]\frac{1}{3}[/tex]×π× 81 units² ×h
135π units³÷ ([tex]\frac{1}{3}[/tex]×π× 81 units²)= h
5 units= h
Finally, the height if the cone is 5 units.
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