Answer:
147.26 cubic units.
Step by step solved:
Let's denote the radius of the base of the cone as r, and the height of the cone as h. We are given that h = 2r and that the base has an area of 25л.
The formula for the volume of a cone is V = (1/3)πr^2h.
Substituting h = 2r, we get V = (1/3)πr^2(2r) = (2/3)πr^3.
We are given that the area of the base is 25л, so we can find r as follows:
πr^2 = 25
r^2 = 25/π
r = √(25/π)
Substituting this value of r into the formula for the volume of the cone, we get:
V = (2/3)π(√(25/π))^3
V = (2/3)π(125/π√π)
V = (2/3)π(125/√π)
= (250/3)√π
= 147.26 cubic units.
Therefore, the volume of the cone is 147.26 cubic units.