Calculate the volume of the solid, bounded by surfaces: z=x^2+y^2; z= 4x^2+4y^2;z=4

- anonymous

Calculate the volume of the solid, bounded by surfaces: z=x^2+y^2; z= 4x^2+4y^2;z=4

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- anonymous

first take 4 common frm 2nd eq then subtract both equation x n y will b canceled n z will be = to 4

- anonymous

Okay.Then?

- anonymous

then by comparin method find the value of x n put it in any of equ then y will automatically come

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## More answers

- anonymous

Okay. Let's say I got the value of x, y and z. How will I calculate the volume? I am a bit rusty on triple integrals.

- anonymous

hmm thts pity difficult :P

- anonymous

multiply all the values didnt u get it?

- anonymous

Well the process I saw online was very difficult and it required a lot more effort. Just multiplication won't help.

- anonymous

ohky m sorry i dnt knw more then that m student of 1st year so0o m sorry :(

- anonymous

It's alright aliza. Thanks for the insight.:)

- anonymous

ur welcome nw m going just pray 4 ma tomorrows NSTC test leaving t,cr

- anonymous

Sure and don't worry you will do well.

- anonymous

:) inshaallah

- anonymous

inshaallah.

- anonymous

\[\int\limits_{0}^{2\pi}\int\limits_{1}^{2}\int\limits_{0}^{4}1 dV\]

- anonymous

|dw:1359821229243:dw|

- anonymous

that would be the projection on the x-y plane?

- anonymous

Okay.

- anonymous

so now try elimination one of x/y and write it interms of z and the other var

- anonymous

i mean y=root(z-x**2)

- anonymous

|dw:1359821411153:dw|
i hope u know how to find the area of the shaded part? i mean in 2-d?
extend it to 3-d adding a dz

- anonymous

fine let's make a guess.............state ur options
i m in no mood to solve it either

- anonymous

2pi,8pi,6pi and 35/4

- anonymous

dose are the options... what do u think wud be a good gess

- anonymous

consider two circles
x**2 + y**2=4 and x**2+y**2=1
what would be the area b/n them?

- anonymous

radius:2 and 1

- anonymous

4pi-pi?
3pi?

- anonymous

so area=3

- anonymous

times 4 and we get 12pi

- anonymous

nope
now it's gone 3d multiply it with 4 #height
ok?
now it's 12 pi
now approximate it to be a cone
now wat's the volume of a cone?

- anonymous

owwww i didnt think of that..

- anonymous

4/3 * 12 * pi
=8*pi ?

- anonymous

1/3(pi)(r^2)(h)

- anonymous

now find the closest answer

- anonymous

8pi

- anonymous

noo sorry it's 1/3 * 12 *pi
4pi
now wat's the closest?

- anonymous

idk deres 2pi and 6pi and 8pi... i gess 2pi then

- anonymous

yup
cone obviously has a larger volume :P
guess that's it @shubhanknigam

- anonymous

Thank you both of you, Tushara and Avinash. You were a big help. Guess I can sleep now.

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