10.2.1 Surface Area of Prisms and Cylinders (continued)
Example 2 Finding Lateral Areas and Surface Areas of Right Cylinders
The lateral area of a cylinder is equal to the circumference of the base times the height of the cylinder. The surface area of a right cylinder is equal to the lateral area plus the areas of the two bases.
The lateral and surface areas of a right cylinder are determined in this example. The circumference is given as 12 π cm and the height is given as 5 r . To calculate the lateral area, begin by determining r by substituting the value for the circumference into the formula for circumference: C = 2 πr , 12 π = 2 πr , therefore r = 6 cm. Since r = 6, the height equals 30 cm. Substituting the values for circumference and height into the formula for lateral area gives 360 π cm 2 . To calculate the surface area, find the area of the base. The area of the base is πr 2 , or 36 π . Substituting the values for the area of the base and the lateral area into the formula for surface area gives a value of 432 π cm 2 .
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