contestada

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

Respuesta :

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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. 
lhmarianateixeira

In this exercise we want to calculate the volume of a circular cone in this way we have that the rotation will be given by:

Letter A

First let's write the rotation in favor of the X, this will be equal to:

[tex]y = x/3\\x = 3y[/tex]

So substituting this value in the function we find that:

[tex]x^2 =(3y)^2= 9y^2\\\int\limits^3_0 {9y^2} \, dx =81 \pi[/tex]

See more about volume at brainly.com/question/1578538

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