Answer: \(\dfrac{4}{3}\pi r^3\)
Step-by-step explanation:
We know that the volume of a cone is given by :-
\(\text{Volume}=\dfrac{1}{3}\pi r^2 h\), where r is radius and h is height of the cone.
Given: Height of cone = 2(2r)=4r , where 2r is the diameter of the cone with radiis r.
Then , the volume of the cone will be:-
\(\text{Volume}=\dfrac{1}{3}\pi r^2 (4r)=\dfrac{4}{3}\pi r^3\)
Hence, the volume of the cone in terms of its base radius r = \(\dfrac{4}{3}\pi r^3\)
