Question

Determine the volume of the right circular cone generated by rotating the line y = 1/3x about the y-axis between y = 0 and y = 3.
A) V = 81pi cu.units
B) V = 84pi cu.units
C) V = 82pi cu.units
D) V = 85pi cu.units
E) V = 83pi cu.units

Answer 1

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Below is the solution:

Rotating around the y-axis; solve for x. y = x/3
x = 3y

Find x^2
x^2 = 9y^2

Integrating it using the limits of 0 and 3, remember to add the pi and integrate 9y^2.

The answer is 81pi cubic units which is A.