Cylinders (Edexcel GCSE Maths): Revision Notes

Cylinders

What is surface area?

Surface area is the total area of all the faces of a 3D shape. For cylinders, you need to work out the areas of all the faces and add them together.

A cylinder has three faces:

• Two flat circular faces (top and bottom)
• One curved face that wraps around the middle

When you imagine flattening out the curved face, it becomes a rectangle. The length of this rectangle equals the circumference of the circle (2πr).

Surface area formula

Surface area = 2 × Area of circle + Area of rectangle

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

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

Where:

• r = radius of the circular base
• h = height of the cylinder

What is volume?

Volume measures how much space is inside a 3D shape. For cylinders, you calculate this by multiplying the area of the base by the height.

Volume formula

Volume of cylinder = Area of base × Height

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

Where:

• r = radius of the circular base
• h = height of the cylinder

Answers in terms of π

Sometimes exam questions ask for exact values or answers in terms of π. When this happens, follow these essential steps:

Example

For a cylinder with radius 3cm and height 4cm:

Volume = πr²h = π × 3² × 4 = 36π cm³

• Exact answer: 36π cm³
• Rounded answer: 113 cm³ (to 3 significant figures)

Exam tips