V = Bh (Circular & Right Circular Cylinders) ER1

Circular Cylinder Definition

A circular cylinder is a cylinder which has a circular right section.

Properties

If a prism whose right section is a regular polygon is inscribed in or circumscribed about a circular cylinder, and if the number of sides of the right section of the prism is indefinitely increased in such a way that every side approaches zero, the volume of the cylinder is the limit of the volume of the prism; the lateral area of the cylinder is the limit of the lateral area of the prism; the perimeter of a base of the cylinder is the limit of the perimeter of a base of the prism.

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Circular Cylinder Formulas

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Lateral area = perimeter of right section x element S = pke Volume = base x altitude V = Bh Volume = right section x element V = Ke

Circular Cylinder
Example 1: A pole in the form of a circular cylinder of altitude 18 ft. and diameter of right section 0.4 ft. has a base whose largest dimension is 0.5 ft. If the pole rolls until it has covered an area of level ground, equal to that of one acre, how many revolutions will it make?

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Circular Cylinder Lateral surface of the pole (NOTE: This is part of the solution, thus, it is not given.)

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Right Circular Cylinder Definition

A right circular cylinder is a circular cylinder whose elements are perpendicular to its base.

Properties

1. The axis of a right circular cylinder is the line joining the centers of the bases. 2. A right circular cylinder may be generated by the revolution of a rectangle about one side as an axis, and is therefore also called a cylinder of revolution. 3. The center of any section of a right circular cylinder parallel to the base is on the axis. 4. Any element of a right circular cylinder is equal to its altitude. 5. Every section of a right circular cylinder made by a plane containing an element is a rectangle.

axis

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Right Circular Cylinder Formulas

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Lateral area = altitude x circumference of base S = pke Volume = base x altitude V = Bh

Right Circular Cylinder
Example 1: An iron pipe 10 ft. long has an internal diameter of 1 ft. If the iron is ½ in. thick, find the volume of metal in the pipe.


Example 2: The diameter of a well is 6 ft., and the water is 7 ft. deep. How many gallons of water are there in the well, reckoning 7.48 gal. to the cubic foot?

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Circular/Right Circular Cylinder HOMEWORK 4 Answer the following problems in 1 whole sheet of yellow paper. Box/encircle your final answers. Deadline is on Feb. 17, 2011 (H). 1.

A straight stairway has a balustrade, with dimensions as shown, containing 2 circular balusters to a step. The foot and hand rails are parallel. Find the total amount of wood used and the total area to be painted, neglecting the rails.

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Circular/Right Circular Cylinder Cont’d… 2.

A pipe manufacturer desires a cylindrical steel drum to hold 50 gal. of roof paint. For convenience in handling, it is found necessary to limit the inside diameter to 2 ½ ft. Find the height of the drum desired. (One gal. = 231 cu. in.)

3. Find the waste in making the largest possible cylindrical rod from a bar of iron 3 ft. long which has a square cross section whose diagonal is 6 in.

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