Question

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

Answer 1

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

Answer 2

Okay.Then?

Answer 3

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

Answer 4

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.

Answer 5

hmm thts pity difficult :P

Answer 6

multiply all the values didnt u get it?

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

Sure and don't worry you will do well.

Answer 12

:) inshaallah

Answer 13

inshaallah.

Answer 14

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

Answer 15

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

Answer 16

Okay.

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

fine let's make a guess.............state ur options

i m in no mood to solve it either

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

radius:2 and 1

Answer 25

4pi-pi?
3pi?

Answer 26

so area=3

Answer 27

times 4 and we get 12pi

Answer 28

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?

Answer 29

owwww i didnt think of that..

Answer 30

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

Answer 31

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

Answer 32

now find the closest answer

Answer 33

8pi

Answer 34

noo sorry it's 1/3 * 12 *pi
4pi

now wat's the closest?

Answer 35

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

Answer 36

yup

cone obviously has a larger volume :P

guess that's it @shubhanknigam

Answer 37

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