SECTION 8.4SURFACE AREA OF A CYLINDER
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REVIEW: AREA AND CIRCUMFERENCE OF CIRCLES
The area of a circle is the space inside the circle
Equation for Area of a Circle = x r x r
[ = 3.14159162] [ ‘r’ is the radius of the circle]
The circumference of a circle is the distance aroundthe perimeter of the circle
Equation for Circumference of a circle = 2 x x r
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Click here to understand why the area of a circle is A=r2
EX: GIVEN THE FOLLOWING CIRCLES, FIND THE AREA ANDCIRCUMFERENCE:
Note: 102 is 10times 10. Not 10times 2!!!
Leaving youranswer as100 is ok
In this circle, wehave the diameterinstead of the radius
Divide the diameterby 2 to get the radius
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WHAT IS A CYLINDER?
A cylinder is a prism where both ends of the solid are circles
Cylinders can be seen in almost everywhere in the world
Ex: Given each object, indicate whether if it is a cylinder or not
No because the circlesat the top & bottomhave different sizes
No because thebottom is not a circle
No because the sideis not straight!!
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SURFACE AREA OF CYLINDERS
The top and bottom of a cylinder arecircles. The equation for the area is
The lateral side of the cylinder is a rectangle.
The height is “h” and the width is thecircumference of the circle
This part is forthe area of bothcircles at the topand bottom
This part is forthe lateral side ofthe cylinder
[Rectangle]
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EX: FIND THE SURFACE OF THE FOLLOWINGCYLINDER
Find the area of both circles
Find the area of the lateral side
Now get the surface area by addingthe area of all three sides
Leaving your answeras 216 cm2 is ok
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PRACTICE FIND THE SURFACE OF THE FOLLOWING SOLIDS:
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The diameter is 8cm. Find the radiusby dividing the diameter by 2
Find the area of both circles
Find the area of the lateral side
Now get the surface area by addingthe area of all three sides
Leaving your answer as 112 cm2 is ok
Ex: A water tower in the shape of a cylinder has radius 10 mand height 30 m. A spiral staircase, with constant slope,circles once around the outside of the water tower. Avertical ladder of height 5 m then extends to the top of thetower. What is the total distance along the staircase and upthe ladder to the top of the tower?
Unwrap the cylinder for the lateral surface
Use the Pythagorean Thm. to findthe length of the diagonal path
The total distance travelled will be:
HOMEWORK:
P 186 #4, 6, 8 – 12
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AREA OF A CIRCLE:
To find the area of a circle, cut it into 8 equal pieces
Put the pieces together to create a parallelogram
The length of the top is equal to half the perimeter
The height is equal to the radius of the circle
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