Assume that Earth is a sphere with a radius of 4500 miles.The center of Earth is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?
A) $2 x ^ { 2 } + 2 y ^ { 2 } + 2 z ^ { 2 } = ( 4500 ) ^ { 2 }$
B) $2 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$
D) $x ^ { 2 } + y ^ { 2 } + 2 z ^ { 2 } = ( 4500 ) ^ { 2 }$
E) $x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$

Question

Assume that Earth is a sphere with a radius of 4500 miles.The center of Earth is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere? 
A) $2 x ^ { 2 } + 2 y ^ { 2 } + 2 z ^ { 2 } = ( 4500 ) ^ { 2 }$
B) $2 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$
D) $x ^ { 2 } + y ^ { 2 } + 2 z ^ { 2 } = ( 4500 ) ^ { 2 }$
E) $x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = ( 4500 ) ^ { 2 }$

Quizplus · Accepted Answer

The equation of a sphere with radius $r$ and center at the origin $(0,0,0)$ in a three-dimensional coordinate system is $x^2 + y^2 + z^2 = r^2$. Given the radius is 4500 miles, the equation becomes $x^2 + y^2 + z^2 = (4500)^2$.

Assume That Earth Is a Sphere with a Radius of 4500