Cylinder

A cylinder is a three-dimensional shape with a pair of parallel and congruent circular ends, called bases.

Cylinders can be right or oblique. The side of a right cylinder is perpendicular to its circular bases.

cylinder

A cylinder has a single curved side that forms a rectangle when laid out flat.

cylindersviluppo

Surface area of a cylinder

cylsurf.png

The area of each base is given by the area of a circle:

areacerchio.png

The area of the rectangular lateral area is given by the product of a width and height. The height is given as h; you can see that the width of the area is equal to the circumference of the circular base.

The circumference of a circle is given by:

circonferenza

Lateral surface is:

suplatcilindro

Inversae formulas:

suplatcilindroinv1       suplatcilindroinv2

Total surface area is:

suptotprisma

Volume of a right cylinder

Right prisms and right cylinders are very similar with respect to volume. In a sense, a cylinder is just a “prism with round bases.”

The volume of a right cylinder with radius r and height h can be expressed as:

volume cil

Inversae formulas:

volume cilinv1         volume cilinv2

Exercises:

  1. Find the volume of the following cylinder:

cil1

2. The radius of the base of a cylinder measures 12 cm and its height exceeds 5 cm three times the radius. Calculate the total surface area and the vol ume of the solid.

3. The lateral surface of a cylinder is of 471 square centimeters. Calculate the volume of the solid knowing that is 15 cm high.

4. The height of a cylinder is 6 cm and the volume is 121.5 pi cubic centimeters. Calculates the lateral surface of the solid.

5. A wedding cake is made of three overlapping cylinders whose diameters are  80 cm, 40 cm and 2 cm and the height of the three cylinders is 12 cm. Find    the total surface area and volume of the cake.

6. In a cylinder is dug prism a square based. Knowing that the height of the cylinder and of the prism measures 20 cm and the radius of the cylinder is 12 cm and the side of a square measures 6 cm, find the total surface area and the volume of the solid.

7. You want to dig a tunnel 12 meters long and 3.5 meters high having the shape of a half cylinder. Calculate the volume of material which must be removed.

8. Calculates the measurement of the radius of a cylinder, knowing that the lateral area is 301.44 squared centimeters and height measures 15 cm.

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