Surface Area and Volume of Cylinders.

The formula for the surface area of a cylinder is the sum of the area of the two bases, and the lateral area. To apply it you need to know the radius of the base, and the perpendicular distance between the two bases, or height. The question is: Would you be able to apply the formula if they don't give you the radius of the base? Or what about that you be given the diameter and the diagonal of the rectangle formed by the diameter and the sides of the cylinder? Would you be able to find the height? What if they gave you the surface area, and the height; but you had to find the radius?

All these types of problems are solved in the examples of this lesson. You will be given the proof for finding the surface area, and the formula for the volume; then you will view examples that range from direct substitution to under the surface questions (Questions that required several steps). You will be in excellent math shape after this lesson!

Lesson's Content

Lesson's Glossary

Base of a conic solid
The planar region that forms the widest point of a conic solid; often labeled as the 'bottom' of the conic solid, it determines the exact shape of the conic solid.

Conic solid
The set of points between a point (the vertex) and a non-coplanar region (the base), including the point and the region.

Cylinder
The surface of a cylindrical solid whose base is a circle.

Cylindrical surface
The union of the bases and the lateral surface.

Diameter of a circle (or sphere)
The segment whose endpoints are points on a circle (or sphere) that contains the center of the circle as its midpoint; the length of that segment.

L.A.
Lateral area.

Lateral area
The area of the lateral surface of a solid.

Lateral surface
The surface not included in the base (s).

Oblique prism or cylinder
A non-right prism or cylinder.

Solid
The union of the surface and the region of space enclosed by a 3-D figure; examples: conic solid, cylindrical solid, rectangular solid.

Solid geometry
The study of figures in three-dimensional space.

Space
The set of all possible points; made up of infinite planes.

Surface
The boundary of a 3-D figure.

Surface area
The total area of the surface of a solid.

Unit cube
Unit of measuring volume.

Interactive Geometric Applets: Relevant Theorems.

Cylinders are similar to prisms. You need to find the base area, and you

have two bases. The difference is that the bases in the cylinder are circles,

and in the prisms are polygons. Practice with this interactive geometric applet

about finding the lateral area, surface area, and volume of a right cylinder.

You may manipulate "r", and "h" to view different sets of problems.

Vocabulary Puzzle Interactive

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