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
๐ Learning Guide
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, as if stacking thin slices of the base up to height :
1. Volume of a Cylinder
A cylinder has a circular base of area and height . Since a cylinder is a prism with a circular base, its volume is found by multiplying this base area by the height:
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 and central angle (in degrees). The volume is the fraction of the full cylinder volume.
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 (cmยณ) or cubic meters (mยณ).
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 ร w ร 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.