Finding the Center and Radius of a Sphere: A Homework Question

[bobbarkernar]

Homework Statement

The equation represents a sphere.

16x^2+16y^2+16z^2-96x+32y=5

Find its center, and radius

Homework Equations

The Attempt at a Solution

i found the center by completing the square:

16[(x^2-6x+9)+(y^2+2y+1)+(z^2)]=5+9+1
16[(x-3)^2 +(y+1)^2 +(z+0)^2]=15

the center is (3,-1,0)
i thought the radius would be (15^.5)/4 but that was incorrect if someone could please help me thank you

 

[chemhelper]

Homework Statement

16[(x^2-6x+9)+(y^2+2y+1)+(z^2)]=5+9+1
16[(x-3)^2 +(y+1)^2 +(z+0)^2]=15

You forgot to multiply the added 1 and 9 on the right side by 16. Either multiply everything out on the left side and see what needs to be added to equalize the right side or try going back and dividing everything by 16 before completing the square.

 

[bobbarkernar]

ok i see what i did wrong. thank you very much