Area and volume of the cylinder


   1. Cylinder parts

    In the picture, we see several examples of cylinders: an oil drum, a drum, a pencil and a flashlight.
    The cylinder has two bases that are two circles and a height which is the perpendicular between the two bases: the side.

    AB side is called generatrix because when it turns on the axis O'O creates the lateral surface of the cylinder.
     Look at this figure and answer:

The segment O'B is...

The segment O'O is...

The segment OA is...

The segment AB is...


    2. - Lateral area of the cylinder

    If we cut the surface of a cylinder by a generatrix and we extend it on a plane, we obtain a rectangle whose base is the length of the circumference of the cylinder base (2 x p x r) and the height is its generatrix. Lateral Area = 2 x p x r x g.
    The lateral area of a cylinder is equal to the product of the length of the circumference of the base by the generatrix or height.

    To find the surface area, we add the lateral area plus the two bases area. The area of a circle is: p x r2
        Surface area = ( 2 x p x r x g ) + ( 2 x p x r2 ). 

    Do these problems on a paper and answer:

1. The radius of the base of a cylinder is 8 cm and its height is twice the diameter. Find the lateral area in cm2.

2. Find the surface area of the previous cylinder.

3. The base diameter of a cylinder is 6 dm. Find the lateral area in dm2 if the height is twice the circumference of the base.

4. Find the surface area of the previous cylinder.

    3. Volume of the cylindernder

    Remember that the volume of a prism is the product of the surface of the base times the height.
    The volume of the cylinder is the product of the area of the circle times the height.
    The area of the circle is  p x r2  . The volume of the cylinder is  p x r2 x height.

    Do these problems on a paper and answer:

1. A cylinder is 5 cm radius base and its height is twice the diameter. Find the volume in cm3 

2. The diameter of the base of a cylinder is 8 m and its height is twice the circumference of the base. Find the volume in m3.

3. The base radius of a cylinder is 4 cm and its height is 3/2 of the circumference of the base. Find the volume in cm3.

4. Find the volume in cm3 of a cylinder of 31.4 cm in circumference and 13 dm height.


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®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999 Plaza Playa de Aro, 3, 1º DO 44002-TERUEL







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