Surface Area and Volume
Volume, curved surface area and total surface area for the cuboid, cube, cylinder, cone, sphere and hemisphere, how the three quantities differ, and how to handle a solid made of two simple shapes.
What you will be able to do
- State the volume, CSA and TSA formula for each standard solid.
- Tell which of volume, curved surface area or total surface area a question wants.
- Convert between cubic units and litres, and keep length units matched.
- Find the surface area of a solid built from two simple shapes by counting the exposed faces.
What is inside this lesson
- 1Three different questions about a solid
- 2Cuboid and cube
- 3Cylinder
- 4Cone, sphere and hemisphere
- 5Solids made of two shapes, and unit care
- 6Worked example
- 7Common mistakes
- 8Quick revision
- 9Practice
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Three different questions about a solid
A solid figure has three quantities that a question can ask for, and they are not interchangeable:
- Volume — the space inside, measured in cubic units. This is what a tank holds or a block weighs.
- Curved (or lateral) surface area, CSA — the area of the side surface only, leaving out the flat top and bottom. This is what a label wraps or a wall of paint covers.
- Total surface area, TSA — every outer face added together, including the top and base.
Read the question for which one it wants: "how much water", "volume" and "capacity" mean volume; "painted", "wrapped", "sheet needed" mean a surface area, and then you decide whether the ends are included.
This topic uses pi = 22/7 when the radius is a multiple of 7 and 3.14159 otherwise.
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