Answer:
[tex]V_{cone}=\frac{1}{3} \,40\,\,ft^3[/tex]
Step-by-step explanation:
I believe you wanted to type that the volume of a cylinder is 40 cubic feet, and try to find what the volume of the same base and height would be in comparison.
Recall that the volume of a cylinder of base B and height H is given by the formula:
[tex]V_{cyl}=B * H[/tex]
Recall as well that the volume of a cone of base B and height H is given by the formula: [tex]V{cone}=\frac{1}{3} B*H[/tex]
Therefore, if the cone has the same base (B) as the cylinder, and equal height (H), then we can say that the volume of the cone is "one third" of the volume of the cylinder, which in Math terms is written as:
[tex]V_{cone}=\frac{1}{3} \,V_{cyl}[/tex]
Therefore, in our case, given that the volume of the cylinder is 40 [tex]ft^3[/tex] , the volume of the cone would be:
[tex]V_{cone}=\frac{1}{3} \,40\,\,ft^3[/tex]
