Cylinders (AQA GCSE Maths): Revision Notes

Cylinders

A cylinder is a 3D shape with two circular faces (called bases) connected by a curved surface. Understanding cylinders is essential for calculating both surface area and volume in real-world applications.

Surface area of cylinders

The surface area of a cylinder is the total area of all its surfaces. When you imagine unrolling a cylinder, you get two circular faces and one rectangular face.

To find the surface area, you need to add up:

• Two circular faces (top and bottom)
• One curved rectangular face (the side when unrolled)

The formula is:

$\text{Surface area} = 2\pi r^2 + 2\pi rh$

Where:

• $r$ = radius of the circular base
• $h$ = height of the cylinder
• $2\pi r^2$ = area of both circular faces
• $2\pi rh$ = area of the curved surface (rectangle)

The width of the rectangular face equals the circumference of the circular base ($2\pi r$), which is why we multiply $2\pi r$ by the height $h$.

Volume of cylinders

The volume of a cylinder measures how much space is inside it. Think of it as the capacity - how much liquid it could hold.

To find the volume:

$\text{Volume} = \pi r^2 h$

This works because:

• $\pi r^2$ = area of the circular base
• $h$ = height of the cylinder
• Volume = base area × height

Working in terms of π

Sometimes exam questions ask for exact answers or answers in terms of π. This means you should leave π as a symbol rather than converting to a decimal.

For example, with a cylinder of radius 3 cm and height 4 cm:

• Exact answer: Volume = $36\pi \text{ cm}^3$
• Rounded answer: Volume = $113 \text{ cm}^3$ (to 3 significant figures)

Key formulas summary

Remember!