Step-by-step explanation:
We have,
Volume of cylinder is 20 ft, [tex]V_1=20\ ft[/tex]
It is required to find the expression that represents the volume of a cone with the same base and height as the cylinder.
Let [tex]V_2[/tex] is volume of cone. The formula of the volume of cylinder and the cone is given by :
[tex]V_1=\pi r^2 h\\\\V_2=\dfrac{1}{3}\pi r^2h[/tex]
Dividing the above formulas as :
[tex]\dfrac{V_2}{V_1}=\dfrac{\dfrac{1}{3}\pi r^2h}{\pi r^2 h}\\\\\dfrac{V_2}{V_1}=\dfrac{1}{3}[/tex]
[tex]V_2=\dfrac{V_1}{3}[/tex]
[tex]V_2=\dfrac{20}{3}\ ft[/tex]
So, the volume of a cone is [tex]\dfrac{20}{3}\ ft[/tex].
