Answer:
The volume of the cone is 10 cubic units
Step-by-step explanation:
Given
Solid Shapes: Cone and Cylinder
Volume of Cylinder = 30 cubic units
Required
Volume of Cone
From the question; we have that the cylinder and the cone has the same height (h) and the same base;
Since they have the same base, then this means they have the same radius.
The Volume (V) of a cylinder is calculated as follows
[tex]V = \pi r^2h[/tex]
Substitute 30 for V
[tex]30 = \pi r^2h[/tex]
The Volume (Vc) of a cylinder is calculated as follows
[tex]V_c = \frac{1}{3} \pi r^2h[/tex]
From the volume of a cone, we have that [tex]\pi r^2h = 30[/tex]; This means that we can substitute 30 for [tex]\pi r^2h[/tex]
[tex]V_c = \frac{1}{3} \pi r^2h[/tex] becomes
[tex]V_c = \frac{1}{3} * 30[/tex]
[tex]V_c = 10[/tex]
Hence, the volume of the cone is 10 cubic units
