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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