Quick questions on Surface area of solids for HSC Maths Standard 2

A right prism has two identical end faces joined by rectangles. The fastest way to its surface area is the net: the two ends plus the band of rectangles wrapped around the sides. For any right prism,

A cylinder is a prism with a circular end. Unroll its curved surface and it becomes a rectangle: its height is the cylinder's height $h$, and its width is the circumference of the circle, $2\pi r$. So the curved surface area is

A sphere is the simplest case to recall and the easiest to over-think. It has a single curved surface and no flat faces, so its surface area is just

A pyramid has a flat base and triangular faces meeting at an apex. Like a prism, there is no formula on the sheet, so build it from the net: the base plus the triangular faces. For a square-based pyramid of base side $a$ with each triangular face having slant height $s$ (the height of the triangular face, measured up the middle of the face),

A cone is the case examiners love, because its formula $A = \pi r l + \pi r^2$ needs the slant height $l$, the straight distance from the apex down the sloping side to the rim, and you are usually given the perpendicular height $h$ instead. The radius, the perpendicular height and the slant height form a right-angled triangle, so Pythagoras gives