Surface Area The region bounded by (x –2)2 + y2 = 1 is revolved about the y-axis to form a torus. Find the surface area of the torus.
To calculate: The surface area of the Torus formed by revolving a region bounded by about the y-axis.
The region bounded by is revolved about the y-axis and a torus is formed.
Formula for differentiation is:
Formula for integration is:
Where, x is a variable and n is a constant value.
Consider the region .
Draw the graph of torus formed by revolving the region bounded by about y-axis with the help of maple:
Let and .
Since, . Differentiate both sides with respect to x,
For the surface area of the torus. Find .
Recall, . Since the torus is symmetrical. Calculate the area of upper half over the interval and multiply by 2
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