## shubhanknigam 2 years ago 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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1. aliza.khan

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

2. shubhanknigam

Okay.Then?

3. aliza.khan

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

4. shubhanknigam

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.

5. aliza.khan

hmm thts pity difficult :P

6. aliza.khan

multiply all the values didnt u get it?

7. shubhanknigam

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

8. aliza.khan

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

9. shubhanknigam

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

10. aliza.khan

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

11. shubhanknigam

Sure and don't worry you will do well.

12. aliza.khan

:) inshaallah

13. shubhanknigam

inshaallah.

14. Tushara

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

15. A.Avinash_Goutham

|dw:1359821229243:dw|

16. A.Avinash_Goutham

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

17. shubhanknigam

Okay.

18. A.Avinash_Goutham

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

19. A.Avinash_Goutham

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

20. A.Avinash_Goutham

|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

21. A.Avinash_Goutham

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

22. Tushara

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

23. Tushara

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

24. A.Avinash_Goutham

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

25. Tushara

26. A.Avinash_Goutham

4pi-pi? 3pi?

27. Tushara

so area=3

28. Tushara

times 4 and we get 12pi

29. A.Avinash_Goutham

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?

30. Tushara

owwww i didnt think of that..

31. A.Avinash_Goutham

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

32. Tushara

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

33. A.Avinash_Goutham

now find the closest answer

34. Tushara

8pi

35. A.Avinash_Goutham

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

36. Tushara

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

37. A.Avinash_Goutham

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

38. shubhanknigam

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