Question

Find equation of the largest possible sphere contained between the planes..
x=-4, x=6, y=2, y=12, z=-3, z=7

Answer 1

the equation of a sphere is (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2

now the distance from x=-4 to x=6 is 10, y=2 to y=12 is 10 and z=-3 to z=7 is also 10 so the radius is 10.

the center point will be exactly half way between each 2 planes so its x value will be 1, y value will be 7 and z value will be 2

plug those numbers into the original equation and you get
(x-1)^2 + (y-7)^2 + (z-2)^2 = 100

Answer 2

The radius would be 5 because the entire sphere is contained between those planes (10 units apart), and the radius is half of that.

Answer 3

Yes, Thank you! I knew I had to find the radius obviously, but I could not picture it, now it makes sense.

Answer 4

the hardest thing with this type of problems is to picture them and figure out how to find the coordinates of the center, once you got that its not too bad :)