Question

Find the volume of the sphere given by the equation:
2x^2+2y^2+2z^2-2x-6y-4z+5=0

Answer 1

\[x^2 + y^2 + z^2 - x - 3y - 2z + \frac52=0\]\[\left(x-\frac12\right)^2 + \left(y -\frac{3}{2}\right)^2 (z-1)^2 -\frac14 - \frac94 -1 + \frac52=0\]
Maybe.

Answer 2

-14/4 + 10/2 = -4/2 = -2
\[\left(x-\frac12\right)^2 + \left(y -\frac{3}{2}\right)^2 (z-1)^2 =(\sqrt2)^2\]
\(\sqrt2\) might be radius. You can calculate volume now.

Answer 3

Ishaan94: almost correct.

Answer 4

Ohh thanks. asnaseer's here :D

Answer 5

LivyLou: what Ishaan94 is trying to do is convert the equation into the general form:\[(x-a)^2+(y-b)^2+(z-c)^2=r^2\]where a, b and c define the centre of the sphere, and r defines its radius.
Once you have the radius, you can use the formula for volume of sphere to get your answer

Answer 6

Ishaan94: you made an error in addition, you should end up with:\[\left(x-\frac12\right)^2 + \left(y -\frac{3}{2}\right)^2+ (z-1)^2 =1^2\]

Answer 7

Ohhh I see.

Answer 8

Thanks for pointing it out

Answer 9

yw

Answer 10

Thanks, but what is the equation to find the volume?

Answer 11

Volume of sphere=\(\displaystyle\frac{4\pi r^3}{3}\)

Answer 12

thanks :)

Answer 13

yw