Answer:
![V=(2)/(3)\pi R^(3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/asa5wv18e3rb618kq1iwawujv90d76p6m5.png)
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)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/an76wgo2ncv6xhlk4rlgx3r9e39zjfakau.png)
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.