There are many options. Amongst them:
An ellipsoid (including a sphere) intersected by two planes which do not, themselves intersect within the shape;
A paraboloid intersected by two planes which do not, themselves intersect within the shape;
A cone intersected by two planes which do not, themselves intersect within the shape;
A semi-hyperboloid intersected by two planes which do not, themselves intersect within the shape;
A toroid (doughnut) intersected by two planes which do not, themselves intersect within the shape;
An elliptic prism intersected by two planes which do not, themselves intersect within the shape.
The last of these would include a cylinder.
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That sounds like a cone. One surface is a circle and the other surface is curved.
Cone
a sphere
I am a geometric solid with one face that is curved. My surface is equally distant from my center at all points. What am I?
A face is any one of the 2-dimensional plane boundaries or surfaces of a solid object. Sometimes the term is also used for curved surfaces.