For the purposes of this question the cone can be treated as a triangle (two back-to-back) right-angled triangles with hypotenuses length 25cm and base of 15/2cm=7.5cm. (A cone is, in any case, a rotated right-angled triangle.) The height is therefore sqrt(25^2-7.5^2)=23.85cm. Does that reasoning sound right according to the mental picture I have? The height is a bit more than the 20cm you estimated.