Cylinder
A cylinder is a solid composed of two congruent circles in parallel planes, their interiors and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions.
The circles and their interiors are the bases . The radius of the cylinder is the radius of a base. The altitude of the cylinder is a perpendicular segment from the plane of one base to the plane of the other and the height of the cylinder is the length of the altitude.
The axis of a cylinder is the segment containing the centers of the two bases. If the axis is perpendicular to the planes of the two bases, the cylinder is a right cylinder ; otherwise, it is an oblique cylinder.
A cylinder is closely related to a prism , so the formulas for their surface areas are related.
Remember the formulas for the lateral
surface area of a prism
is
and the total surface area is
. Since the base of a cylinder is a circle, we substitute
for
and
for
where
is the radius of the base of the cylinder.
So, the formula for the
lateral
surface area of a cylinder
is
. (The lateral surface of a cylinder when unwrapped and laid flat is a rectangle whose dimensions are the height of the cylinder and the circumference of the base.)
Example 1:
Find the lateral surface area of a cylinder with a base radius of
inches and a height of
inches.
The general formula for the
total surface area
of a cylinder is
.
Example 2:
Find the total surface area of a cylinder with a base radius of
inches and a height of
inches.
The
volume
of a cylinder equals the area of a base times the height of the cylinder
(
).
Example 3:
Find the volume of a cylinder with radius
cm and height
cm.
- A Level Digital Technology Tutors
- SAS Programming Training
- International Law Tutors
- Cardiology Tutors
- Pre-Calculus for Business Tutors
- Allied Health Certification Tutors
- Life Science Calculus Tutors
- Anthropology Tutors
- CLEP Introductory Business Law Tutors
- Idaho Bar Exam Courses & Classes
- MCSD - Microsoft Certified Solutions Developer Courses & Classes
- Latin Tutors
- Discrete Math Tutors
- CAE - Certified Association Executive Exam Test Prep
- GRE Test Prep
- GIS Mapping Tutors
- Florida EOC Assessment Courses & Classes
- Elementary Social Studies Tutors
- ARRT Test Prep
- OAT Physics Courses & Classes
- San Francisco-Bay Area Tutoring
- Cincinnati Tutoring
- Buffalo Tutoring
- Pittsburgh Tutoring
- Tucson Tutoring
- Philadelphia Tutoring
- Orlando Tutoring
- Madison Tutoring
- Phoenix Tutoring
- Virginia Beach Tutoring