Surface area is the sum of a solid's external faces — a 2D measurement, so always in square units ($\text{cm}^2$). Volume is the space inside — a 3D measurement, in cubic units. Confusing the two (or giving a volume answer in $\text{cm}^2$) is one of the most common errors in this topic — before calculating anything, decide which one the question is actually asking for.

A cuboid has six faces in three identical pairs. Calculate each of the three unique face areas (length×width, length×height, width×height), then double the total:

Split the calculation into two parts: the two identical end faces, and the "wrapped around" lateral faces. The lateral area is simply the cross-section's perimeter multiplied by the prism's length:

For a triangular prism, this means finding the triangle's area and perimeter first (Pythagoras may be needed if a side isn't given directly), then applying this formula — much faster than calculating five separate rectangular faces individually.

The net of a cylinder is two circles plus one rectangle (the curved surface, unrolled). The rectangle's height is the cylinder's height $h$, and its width is the circle's circumference, $2\pi r$:

Read the context carefully before choosing a formula:

An open-top cylinder, for instance, needs $\pi r^2 + 2\pi rh$ (one base, not two).

Never simply add the full surface areas of the two component shapes — wherever they join, that internal face is no longer exposed and must be excluded from both pieces. Only the newly visible external surfaces count.

Because area is a squared dimension, the conversion factor must also be squared: since $1\text{ m}=100\text{ cm}$, it follows that $1\text{ m}^2=100^2=10{,}000\text{ cm}^2$. Applying the linear factor (×100) instead of the area factor (×10,000) is a common and costly error — convert the linear dimensions to the same unit before squaring, to avoid it entirely.

A closed cylindrical tin has radius 4 cm and height 10 cm. Find its total surface area in terms of $\pi$, then as a decimal to 1 d.p.

1. Curved surface area: $2\pi rh = 2\pi(4)(10)=80\pi$.
2. Two circular bases: $2\pi r^2=2\pi(16)=32\pi$.
3. Total: $80\pi+32\pi=112\pi \text{ cm}^2$.
4. As a decimal: $112\pi \approx 351.9 \text{ cm}^2$ (1 d.p.).