Geometry: Understanding General Cylinders and Their Properties, Study notes of Advanced Calculus

Download Geometry: Understanding General Cylinders and Their Properties and more Study notes Advanced Calculus in PDF only on Docsity!

2. If the lateral edges of a general cylinder are perpendicular to the base, the figure is a right figure.
   3. If the base of a general cylinder is a polygon, then the general cylinder is called a prism.
3. A general cylinder with a circle for a base is called a circular cylinder. The term "cylinder" refers to a right circular cylinder. Complete:
4. A general cylinder with a polygonal base is called a ______________.
5. A general cylinder with a circular base is called a ______________________.
6. A general cylinder with lateral edges perpendicular to the base is a _________ general cylinder.
7. A general cylinder with lateral edges not perpendicular to the base is an ______________ general cylinder.

• 1. The shape of a base of a general cylinder can be a curved shape or a polygon. A B (^) C D E G^ F H base Name the two bases : _________ and __________ Name the 4 lateral edges: ___ ___ ___ ___ Name the 8 base edges: ___ ___ ___ ___ ___ ___ ADFG is a lateral face. ___ ___ Name the 3 other lateral faces: _____ _____ _____

7. Consider the right rectangular prism on the right. If the lateral edges are not perpendicular to the base, the figure is oblique. General Cylinder Facts
8. Name the prism.
   6. Is this a cylinder? Explain why or why not.

Definition : A cross-section of a general cylinder is the intersection of the

general cylinder with a plane.

Exercise: Sketch a cross-section (two dimensional drawing) that is parallel to

the base and one that is perpendicular to the base for the following figures:

Total Surface Area of a right general cylinder = Lateral Area + Area of two bases

Lateral Surface area of a right general cylinder = height perimeter of a base

Using a Cross Section of a General Cylinder to find Surface Area and Volume

A cylinder - right or oblique - can be seen as a stacking of congruent cross sections,

which are parallel to the base.

The LATERAL SURFACE AREA ("shell") of a right circular cylinder or a right

general cylinder is the product of the perimeter of one cross section and the

height of the cylinder. In a cylinder, perimeter = circumference.

h

The VOLUME of the cylinder is the product of the area of one cross section

that is parallel to the base and the height of the cylinder.

Volume of a right or oblique cylinder = height area of a base

5. A right prism has base area 5 ft 2 and volume 20 ft 3 . Find the prism's height, h.
6. A fish tank in the shape of a rectangular prism has dimensions of 7 in., 12 in., and 5 in. The tank currently has 280 cubic inches of water. What percent of the fish tank is filled with water?
7. A POD is in the shape of a rectangular prism and has dimensions of 16 ft by 8 ft by 8 ft. If filled, the contents weigh, on average, 0.25 pounds per cubic foot. What is the weight, in pounds, of the contents of the POD?
8. Sketch the figure formed if the region is rotated around the provided axis. Let's Sum it Up!

• General cylinders may have a curved base or polygonal base or a combination of curves and segments.
• Cylinders are right circular cylinders whose bases are circles.
• Prisms are general cylinders with polygonal bases.
• The lateral area of a general cylinder is the product of the perimeter of the base times the height of the cylinder.
• The volume of a general cylinder is the product of the area of the base times the height of the cylinder.

8. What figure is generated by the rotation of a rectangle along one of its sides?

Name_____________________________ CC Geometry H

Date ____________________ HW

2) A gallon of paint covers approximately 450 square feet. The following right

general cylinder has a lateral edge length of 12 ft and the perimeter of its base is

500 ft. An artist wants to paint the lateral area. What is the least number of

gallons of paint she must buy to paint the area?

1) The base of the following cylinder has a circumference of 8 π in. and a lateral

edge of 12 in. What is the radius of the base? What is the lateral area of the

cylinder (in terms of π)?

5) A right square prism has base edge 6 cm and height 24 cm. Find the volume of

the prism.

3) For the following cross-section, which is parallel to the base of the solid, sketch

the solid from which the cross-section was taken.

4) If the rectangle below is rotated about side x, what solid is formed?

x