areas and volumes
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Areas and Volumes
Area of a circle
Area of a circle
Area of a circle
Area of a circle
We need a substitution
Find the limit points
Replace
Replace
Volume of a sphere
Area of ellipse- use parametric equations
The Rings of the Lord
w/2r
R
The Rings of the Lord
• Volume =
w/2r
R
• Volume =
w/2r
R
Arc length
Arc length
You need a substitution
You need a substitution
A cable of length l is suspended between two towers of equal height a distance 2d apart, so that it sags a distance h in the
centre.
– The curve formed by a suspended rope or cable is called a catenary. Using a coordinate system with the lowest point of the catenary at the origin, it can be described by the equation
– where a is a constant
• Use the arc length formula to show that
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