contestada

The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?

Respuesta :

konrad509

[tex]V=\dfrac{1}{3}\pi r^2h\\\\h=2r\\V=\dfrac{1}{3}\pi r^2\cdot(2r)=\dfrac{2}{3}\pi r^3[/tex]

profantoniofonte

Answer:

[tex]V=\frac{2}{3}\pi R^{3}[/tex]

Step-by-step explanation:

The Volume of a cone is by definition 1/3 of the volume of a Cylinder. In this question, the height equals to diameter (2R).

So, We have:

[tex]h_{cone}=2R\\V=\frac{1}{3}\pi R^{2}h \Rightarrow V=\frac{1}{3}\pi R^{2}2R \Rightarrow V=\frac{2}{3}\pi R^{3}[/tex]

We conclude that under this circumstance, a cone with a height equal to its diameter will turn its volume to be equal to 2/3 of pi times the radius raised to the third power.

In other words, when the height is equal to the diameter. The relation between radius, height and Volume changes completely.