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 hh and width equal to the base's perimeter PP):

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 hh and length equal to the circle's circumference 2πr2\pi r):

Cylinder

A cylinder is a three-dimensional solid with two parallel, congruent circular bases connected by a curved surface.

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

hrTop Base Sticker (πr²)Bottom Base Sticker (πr²)Side Sticker(2πr × h)Length 2πrh

Surface Area of a Cylinder

A=2πr2+2πrhA = 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 θ360∘πr2\frac{\theta}{360^\circ} \pi r^2, giving a total base area of 2×θ360∘πr2=θ180∘πr22 \times \frac{\theta}{360^\circ} \pi r^2 = \frac{\theta}{180^\circ} \pi r^2.
  • Two flat rectangular side faces: each rectangle has width rr and height hh, giving a total area of 2×rh2 \times r h.
  • One curved lateral face: a rectangular sticker of height hh and length equal to the sector's arc length θ180∘πr\frac{\theta}{180^\circ} \pi r, giving an area of θ180∘πrh\frac{\theta}{180^\circ} \pi r h.

Cylinder Sector (Wedge)

A cylinder sector prism (cylinder wedge) is a fraction of a full cylinder.

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

Top Sector BaseBottom Sector BaseFlat Side (r × h)Flat Side (r × h)Curved Side(πrθ/180 × h)Length πrθ/180

Surface Area of a Cylinder Sector

A=2×(θ360∘πr2)+2rh+θ180∘πrhA = 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 rr, central angle θ\theta in degrees, and height hh.
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.

Surface Area of a Cylinder — Practice & Guide | SealMath