Easy solids of revolution clarification

[cesaruelas]

Homework Statement

Calculate the volume of the solid of revolution formed when you rotate region R, delimited by f(x) = x^2 from x = 0 to x = 3, around:
a)the x axis
b) the y axis

The Attempt at a Solution

I solved it using the disc method.

a) dV = pi * x^4 * dx. thus V = (pi* x^5)/5 + c from x=0 to x=3. thus V=152.68 cubic units.

b) since f(y) = y^(1/2), dV = pi * y * dy. thus V = (pi * y^2)/2 + c from y = 0 to y = 9. thus V = 127.23 cubic units.

My question is: Isn´t the volume when I rotate it along either the x or y-axis supposed to be the same? If it is so, I can´t find where I went wrong.

 

[Dick]

Homework Statement

Calculate the volume of the solid of revolution formed when you rotate region R, delimited by f(x) = x^2 from x = 0 to x = 3, around:
a)the x axis
b) the y axis

The Attempt at a Solution

I solved it using the disc method.

a) dV = pi * x^4 * dx. thus V = (pi* x^5)/5 + c from x=0 to x=3. thus V=152.68 cubic units.

b) since f(y) = y^(1/2), dV = pi * y * dy. thus V = (pi * y^2)/2 + c from y = 0 to y = 9. thus V = 127.23 cubic units.

My question is: Isn´t the volume when I rotate it along either the x or y-axis supposed to be the same? If it is so, I can´t find where I went wrong.

No, they aren't supposed to be the same at all. Draw a sketch of the solids. They look pretty different, don't they?