The base can be any shape: if it is a polygon the shape is called a pyramid. The cones you will see in exams will be circular based. The formulas for the volume and surface area of a cone will be ...
The formula for the volume and surface area of a sphere will be given to you in the exam, so you will not need to memorise these. \(\text{The volume of a sphere} ~=~ \frac {4}{3} \times \pi \times ...