WATER PLANT OPERATOR TRAINING PROGRAM

SURFACE AREA AND VOLUME

(pi = = 3.141592...)

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Surface Area

To find the surface area of a cylinder add the surface area of each end plus the surface area of the side. The surface area of each end is the r2. There are two ends so their combinded surface area is 2*r2. The surface area of the side is the circumference times the height or 2rh. The entire formula for the surface area of a cylinder is 2*r2 + 2rh.

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Volume

cylinder = b h = pi r ² h

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Surface area is the total of the areas of all the surfaces of a figure. The formulas used above for area calculations are also used to calculate surface areas. First the figure must be broken down into its component parts, then the total area of these parts must be calculated.

Cylinders

The surface of a cylinder is composed of 3 parts: the top surface (a circle), the bottom surface (a circle), and the curved side surface (a rectangle). The areas of the top and bottom surfaces are the same, and can be calculated using the formulas for the area of a circle.

Area = D2 /4 or Area = R2

The area of the side surface can be determined by imagining that the side surface is unrolled into a rectangle as illustrated below. The length of the rectangle is equal to the circumference of the top or bottom circle, and the width is the height of the cylinder.

Area = D H or Area = 2 R H

The surface area of a cylinder is the total of these 3 areas.

Example: Find the total surface area of a cylindrical tank with a base diameter of 18 meters and a height of 4 meters.

1. Find the area of the top surface
Area = D² /4
= (3.1416) x (18m) 2/4
= 254.5m²

2. Find the area of the bottom surface
Area = D² / 4
= 254.5 m²

3. Find the area of the side surface
Area = D x H
= 3.1416 x 18 m x 4 m
= 226.2 m²

4. Find the total surface area
Surface area = 254.5 m² + 254.5 m² = 226.2 m²

= 735 m²