Answer:
The volume of the cylinder is [tex]300\pi[/tex] cubic feet.
Step-by-step explanation:
From Geometry we remember that volumes of a cone and a cylinder with the same radius ([tex]R[/tex]), measured in feet, and height ([tex]h[/tex]), measured in feet, are defined by the following equations:
Cone
[tex]V_{co} = \frac{1}{3}\pi\cdot R^{2}\cdot h[/tex] (1)
Cylinder
[tex]V_{cy} = \pi\cdot R^{2}\cdot h[/tex] (2)
The ratio of the volume of the cylinder to the volume of the cone is:
[tex]\frac{V_{cy}}{V_{co}} = 3[/tex] (3)
If we know that [tex]V_{co} = 100\pi\,ft^{3}[/tex], then the volume of the cylinder is:
[tex]V_{cy} = 3\cdot V_{co}[/tex]
[tex]V_{cy} = 300\pi\,ft^{3}[/tex]
The volume of the cylinder is [tex]300\pi[/tex] cubic feet.
