Surface Areas and Volumes - Cylinders

1!Michelle Churchill ED569 Spring 2013

Circular Cylinder What Real-World Shapes Are We Talking About?

beverage can, oil drum, paint can

A Cylinder is

A geometric figure with straight parallel sides and a circular top and bottom

Michelle Churchill ED569 Spring 2013

Circular Cylinder - Activity

Fold your Cylinder

Label A1, A2,

and r, h, and C

on your cylinder.

A1

A2

r

C

C

A1

h

Michelle Churchill ED569 Spring 2013

4!

Circular Cylinder

•  Surface Area (SA) of this Cylinder breaks down into 2 Circles and a rectangle

•  2 same sized circles - A1 1 rectangle - A2

•  Area of a Circle, A1 = πr2

•  Circumference of a circle; C = 2πr

•  Area of a Rectangle is A2 = l • w; l = h, height of cylinder and w = C, the circumference of the circle

•  Surface Area of a Cylinder is SA = 2(A1)+ A2 SA = 2 πr2 + 2πrh

A1

A2 h

r

C

C

A1

Michelle Churchill ED569 Spring 2013

Circular Cylinder – Sample Problem •  r = 5 in; h =15 in;

•  A1 = πr2 = π52 = 78.5 in2

•  C = 2πr = 2π5 w = C = 31.4 in2

•  Area of a Rectangle as: A2 = h • w

•  A2 = (15 in) (31.4 in) = 471.24 in2

•  Surface Area of this cylinder is SA = 2 (A1)+ A2

•  SA = 78.5 in2 + 471.24 in2 SA = 549.74 in2

A1

A2 15 in

5 in

C

C

A1

Units!! Michelle Churchill

ED569 Spring 2013

6!

Volume of a Circular Cylinder

•  Volume of a circular cylinder is the area of a base, a circle, multiplied by the cylinder height

•  Area of the Circle = πr2

•  Volume = πr2h

Michelle Churchill ED569 Spring 2013

7!

Volume of a Circular Cylinder – Sample Problem

•  Area of the Circle = πr2

•  Volume = πr2h

•  Volume of the given cylinder is V = π•52•15 V = 1,178 in3

r = 5 in h = 15 in

Michelle Churchill ED569 Spring 2013

8!

Summary Formulas

Cylinder

Surface Area (SA) SA = 2 πr2 + 2πrh

or SA = 2 (A1)+ A2

Volume

V = πr2h

Area Unit = (unit)2

Volume Unit = (unit)3

When Doing Problems, Show All Work and Don’t Forget the Units!!

A1

A2

r

C

C

A1

h

Michelle Churchill ED569 Spring 2013