32.9k views
3 votes
The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?

User Leon Xiong
by
5.0k points

2 Answers

2 votes


V=(1)/(3)\pi r^2h\\\\h=2r\\V=(1)/(3)\pi r^2\cdot(2r)=(2)/(3)\pi r^3

2 votes

Answer:


V=(2)/(3)\pi R^(3)

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:


h_(cone)=2R\\V=(1)/(3)\pi R^(2)h \Rightarrow V=(1)/(3)\pi R^(2)2R \Rightarrow V=(2)/(3)\pi R^(3)

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.

User Kourosh
by
4.7k points