Take note Theorem 11-2: Lateral and Surface Areas of a Cylinder

The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.

L.A. = 2 π r · h , cap l.cap a. , equals 2 , pi r middle dot h comma or L.A. = π d h cap l.cap a. , equals pi d h

The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases.

S.A. = L.A. + 2 B , cap s.cap a. , equals , cap l.cap a. , plus 2 b comma or S.A. = 2 π r h + 2 π r 2 cap s.cap a. , equals 2 pi r h plus 2 pi , r squared

Problem 3 Finding Surface Area of a Cylinder

Multiple Choice The radius of the base of a cylinder is 4 in. and its height is 6 in. What is the surface area of the cylinder in terms of π ? pi question mark

1. 32 π  in . 2 32 pi in , . squared
2. 42 π  in . 2 42 pi . in , . squared
3. 80 π  in . 2 80 pi in , . squared
4. 120 π  in . 2 120 pi in , . squared

S.A. = L.A. + 2 B Use the formula for surface area of a cylinder. = 2 π r h + 2 ( π r 2 ) Substitute the formulas for lateral area and area of a circle. = 2 π ( 4 ) ( 6 ) + 2 ( π 4 2 ) Substitute  4  for  r  and  6  for  h . = 48 π + 32 π Simplify. = 80 π   table with 5 rows and 3 columns , row1 column 1 , cap s.cap a. , equals , column 2 cap l.cap a. . plus 2 b , column 3 cap usetheformulaforsurfaceareaofacylinder. , row2 column 1 , equals , column 2 2 pi r h , plus 2 , open pi , r squared , close , column 3 cap substitutetheformulasforlateralareaandareaofacircle. , row3 column 1 , equals , column 2 2 pi open 4 close open 6 close , plus 2 , open pi , 4 squared , close , column 3 cap substitute . 4 , for , r , and , 6 , for , h . , row4 column 1 , equals , column 2 48 pi , plus 32 , pi , column 3 cap simplify. , row5 column 1 , equals , column 2 80 pi , column 3 , end table

The surface area of the cylinder is 80 π  in . 2 . 80 pi . in , . squared , . The correct choice is C.

✓ Got It?

3. A cylinder has a height of 9 cm and a radius of 10 cm. What is the surface area of the cylinder in terms of π ? pi question mark