Volume & Surface Area: Volume of a Cylinder

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

Practice

📖 Learning Guide

Prism

A prism is a three-dimensional solid with a constant cross-section (base).

Volume of a General Prism

V = \text{Base Area} \times \text{height}

A prism is a three-dimensional solid with a constant cross-section (base). The volume of any prism is calculated by multiplying the area of its base by its height.

1. Volume of a Cylinder

A cylinder has a circular base of area

A = \pi r^2

and height

h

. Since a cylinder is a prism with a circular base, its volume is found by multiplying this base area by the height:

Cylinder

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

Volume of a Cylinder

V = \pi r^2 h

2. Volume of a Cylinder Sector

A cylinder sector prism (cylinder wedge) is a fraction of a full cylinder. Its base is a sector with radius

r

and central angle

\theta

(in degrees). The volume is the fraction of the full cylinder volume.

Cylinder Sector (Wedge)

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

Volume of a Cylinder Sector

V = \frac{\theta}{360^\circ} \pi r^2 h

Calculated using radius

r

\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 cylinder?

The volume of a cylinder is calculated by multiplying the area of its circular base by its height:

V = \pi r^2 h

.