A scientist performs an experiment to produce a compound by adding various amounts of a catalyst to a chemical reaction. Her dat
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Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
The image of G after dilation is G'(5,-5). So,
On comparing both sides, we get
So, the scale factor is .
Substituting in (i), we get
Therefore, the required algebraic representation to represents this dilation is .
Using shells, the volume is
where
is the distance from any point in the region along the x-axis to the axis of revolution 
, which makes up the radius of each shell; and 
is the height of each shell, which is determined by the line 
.
So the volume is
where
So the volume is