Question

Write down an (in)equality which describes the solid ball of radius 66 centered at (10,−10,−7).(10,−10,−7). It should have a form like x2+y2+(z−2)2−4>=0x2+y2+(z−2)2−4>=0, where you use one of the following symbols ≤,<,=,≥,>≤,<,=,≥,>.

Answer 1

Equation of solid ball is
`(x-10)^2+(y+10)^2+(z-7)^2\leq 4356`.

Explanation:

A equation of a solid ball centered at (a,b,c) with radious r is of the form,

`(x-a)^2+(y-b)^2+(z-c)^2-r^2\leq 0`

Here
`(\leq)` takes the inner region and outer surfaces of the solid. So in this problem center (a,b,c)=(10,-10,-7) and radious r=66, then equation of required solid ball is,

`(x-10)^2+(y+10)^2+(z-7)^2-(66)^2\leq 0`

`\implies(x-10)^2+(y+10)^2+(z-7)^2\leq 4356`