We would need one other piece of information to answer it:
EG. the angle of the slope, or the radius or diameter of the cone base, or perhaps, the volume of the cone would also help.
We need just one of these aforesaid pieces of information in order to calculate height.
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A cone with a base of 9 cm and a height of 12 cm has a volume of 254.469 cm3
The cross section will be a triangle with base 2 feet and a vertical height of 9 feet.
For a right circular cone, the lateral area is 565.49 units2
For a right circular cone: Vol. of cone = (PI*r2*h)/3 Vol. = (PI*(9)2*(11))/3 Vol. approx. = 933.1 cubic units
The volume of a cone of radius 12 and height 71 is 10706.54776 cubic units.