Question

49. In three dimensions, what is the measure of the diameter of the sphere x² + y² +z²+2x-2y-6z-14=0 A. 10 units B. 12 units C. 14 units D. 6 units​

Answer 1

A. 10 units Hope This Helps ;D

Explanation:

Sphere - Definition, Formulas, Equation, Properties & Examples

Unlike a circle, which is a plane shape or flat shape, defined in XY plane, a sphere is defined in three dimensions, i.e. x-axis, y-axis and z-axis.

Answer 2

Answer: A. 10 units

Explanation:

Equation of a sphere with radius R and center at a point with coordinates (x₀, y₀, z₀) in the Cartesian coordinate system:

`\boxed{(x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = R^2}`

`x^2+y^2+z^2+2x-2y-6z-14=0\\\\(x^2+2x+1)+(y^2-2y+1)+(z^2-2*3y+9)-11-14=0\\\\(x+1)^2+(y-1)^2+(z-3)^2-25=0\\\\(x+1)^2+(y-1)^2+(z-3)^2=25\\\\(x+1)^2+(y-1)^2+(z-3)^2=5^2\ \ \ \ \ \ \Rightarrow\\\\R=5.\\\\D=2R\\\\D=2*5\\\\D=10 \ units`