Volume problem (1 Viewer)

[Nerd Queen]

Hey can any one help me with this volume problem i dont think i am getting the right answer.

ok so there is a diagram of a straight line which cuts the x-axis at -2 and the y-axis at 4, obviously its equation is y=2x+4. On the diagram the area between the line and the 2 axis' is shaded

then it says:

The area shaded is rotated about the y- axis to form a cone. Find the exact volume of that cone. Check your answer by a second method.


so anyway the second method i used was the area of a cone and got

V= 1/3*pi*4*4
= 16(pi)/3 (as exact volume)

The first method I used however, (around the y-axis thing) is giving me, not only a different answer but a negative answer what am i doing wrong?

this is what i did:

y=2x+4
2x = y-4
x = (y-4)/2
x^2 = (y^2 - 16)/4

I had it rotated about the y-axis between y=4 and y=0 (is this right?) hence:

integrating gave: {[(y^3)/12] - 4y}

so: V= (pi){([4^3/12] - 4(4)) - 0}
= -32(pi)/3

What am i doing wrong?

is it between Y=4 and Y=0?

is the volume of a cone thing i used right?

why am i getting a negative? that has never happened b4? i am really really confused

sorry to be a burden

but help would be appriciated by anyone!

 

[shafqat]

x = (y-4)/2
x^2 = (y^2 - 16)/4

what is (y-4)^2?

 

[Nerd Queen]

oh my god! ITS OFFICIAL, i am an idiot!

(y-4)^2 = y^2 - 8y +16

THANX so much ur a lifesaver i cant believe i screwed that up!

I got the answer now

16(pi)/3

Thanx THanx THAnx THANx THANX