Volume & Surface Area: Surface Area of a Cylinder

Learn how to calculate the surface area of a cylinder, sector prisms, and composite shapes. Practice exercises with step-by-step solutions.

Practice

📖 Learning Guide

The total surface area of any prism is the sum of the areas of all its outer boundaries. This consists of the two bases (top and bottom) plus the area of the lateral side walls (which, when unfolded, form a large rectangle of height

h

and width equal to the base's perimeter

P

Surface Area of a General Prism

A = 2 \times \text{Base Area} + \text{Perimeter} \times \text{Height}

1. Surface Area of a Cylinder

The surface area of a cylinder is the total area of its outer boundaries. It consists of the areas of the two circular bases plus the area of the curved lateral surface (which, when unfolded/unwrapped, is a rectangle of height

h

and length equal to the circle's circumference

2\pi r

💡 Circular stickers for the Top and Bottom bases, and a flat rectangular sticker for the curved side hovering outside.

Surface Area of a Cylinder

A = 2\pi r^2 + 2\pi r h

2. Surface Area of a Cylinder Sector

For a cylinder sector prism (cylinder wedge), its outer boundary consists of:

Two sector bases: each sector has area $\frac{\theta}{360^\circ} \pi r^2$ , giving a total base area of $2 \times \frac{\theta}{360^\circ} \pi r^2 = \frac{\theta}{180^\circ} \pi r^2$ .
Two flat rectangular side faces: each rectangle has width $r$ and height $h$ , giving a total area of $2 \times r h$ .
One curved lateral face: a rectangular sticker of height $h$ and length equal to the sector's arc length $\frac{\theta}{180^\circ} \pi r$ , giving an area of $\frac{\theta}{180^\circ} \pi r h$ .

💡 Two sector stickers, two rectangle stickers for the flat sides, and one curved sticker of length $\pi r \theta / 180$ hovering outside.

Surface Area of a Cylinder Sector

A = 2 \times \left(\frac{\theta}{360^\circ} \pi r^2\right) + 2 r h + \frac{\theta}{180^\circ} \pi r h

Calculated using base radius

r

, central angle

\theta

in degrees, and height

h

Learning Topics

Frequently Asked Questions

What is volume?

Volume is the amount of three-dimensional space occupied by an object. It is measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

How do you calculate the volume of a box?

The volume of a box (rectangular prism) is calculated by multiplying its length, width, and height: V = l × w × h.

What is the surface area of a shape?

Surface area is the total area of all the exterior faces of a 3D shape. It represents how many square units are needed to completely cover the outside of the shape without any overlaps.

How do you calculate the surface area of a cylinder?

The surface area of a cylinder is the sum of the areas of its two circular bases and its curved lateral surface: $A = 2\pi r^2 + 2\pi r h$.