Surface Areas and Volumes Mind Map

The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.

If the question says only the side, label, cover, or curved part, use 2πrh and do not add the bases.

The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.

When the cylinder is closed or all outer surfaces are mentioned, use 2πr(h+r).

The volume of a cylinder is the amount of space enclosed inside it.

For capacity or space inside a cylinder, always use πr²h and write cubic units.

The curved surface area of a cone is the area of its sloping side, excluding the circular base.

If only the side of the cone is covered, use πrl and remember that l means slant height.

The total surface area of a cone is the area of its curved surface plus the area of its circular base.

If the question says whole outer surface or complete covering, use πr(l+r).

The volume of a cone is one-third of the volume of a cylinder having the same base radius and height.

For cone volume, height must be perpendicular to the base, not the slant height.

The surface area of a sphere is the total area of its outer curved surface.

For any sphere, remember that only the radius is needed: 4πr².

The volume of a sphere is the amount of space enclosed inside it.

For sphere volume, remember the fraction 4/3 and the cube of the radius.

The surface area of a hemisphere is the curved surface plus the circular base when the whole outer surface is asked for.

Read the wording carefully: curved surface only means 2πr², but total surface area means 3πr².

The volume of a hemisphere is half the volume of a sphere with the same radius.

A hemisphere is half a sphere, so its volume is 2/3 πr³, not 1/3 πr³.

When one solid is melted, recast, or reshaped into another solid without wastage, the volume of material remains the same.

In recasting questions, write volume before and after as equal, then substitute the correct formulas.

A combination of solids is a shape formed by joining two or more simple solids together.

First split the object into simple solids, then add volumes or exposed areas carefully.