Chapter 11, Problem 18RE

To determine

To find : The standard equation of the sphere with the given characteristics.

Answer to Problem 18RE

  ${\left(x+3\right)}^2+{\left(y-4\right)}^2+{\left(z+1\right)}^2=9^2$

Explanation of Solution

Given information: Center of the sphere is $\left(-3,4,-1\right)$ and diameter is 18.

Calculation:

Diameter of the sphere is 18, and so radius is $\frac{18}{2}$ , that is 9.

We know that standard form of equation of sphere with center $\left(a,b,c\right)$ and radius r is

  ${\left(x-a\right)}^2+{\left(y-b\right)}^2+{\left(z-c\right)}^2=r^2$

Therefore, equation of sphere with center $\left(-3,4,-1\right)$ and radius 9 is

  ${\left(x+3\right)}^2+{\left(y-4\right)}^2+{\left(z+1\right)}^2=9^2$