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

shubhanknigam
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Okay.Then?

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

shubhanknigam
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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.

aliza.khan
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hmm thts pity difficult :P

aliza.khan
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multiply all the values didnt u get it?

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

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

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

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

shubhanknigam
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Sure and don't worry you will do well.

aliza.khan
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:) inshaallah

shubhanknigam
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inshaallah.

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

A.Avinash_Goutham
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dw:1359821229243:dw

A.Avinash_Goutham
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that would be the projection on the xy plane?

shubhanknigam
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Okay.

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

A.Avinash_Goutham
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i mean y=root(zx**2)

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

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

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

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

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

Tushara
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radius:2 and 1

A.Avinash_Goutham
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4pipi?
3pi?

Tushara
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so area=3

Tushara
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times 4 and we get 12pi

A.Avinash_Goutham
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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?

Tushara
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owwww i didnt think of that..

A.Avinash_Goutham
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4/3 * 12 * pi
=8*pi ?

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

A.Avinash_Goutham
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now find the closest answer

Tushara
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8pi

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

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

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

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