A spherical building has a diameter of $201$ feet.The center of the building is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?
A) $x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = \frac { 40,401 } { 4 }$
B) $2 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = \frac { 40,401 } { 4 }$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = \frac { 40,401 } { 4 }$
D) $4 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = \frac { 40,401 } { 4 }$
E) $x ^ { 2 } + 2 y ^ { 2 } + 4 z ^ { 2 } = \frac { 40,401 } { 4 }$

Question

Quizplus · Accepted Answer

The equation of a sphere with center at the origin and radius $r$ is $x^2 + y^2 + z^2 = r^2$. The diameter of the sphere is $201$ feet, so the radius is $201/2 = 100.5$ feet. Squaring the radius gives $100.5^2 = 10,100.25$, which is not directly given in any of the options. However, the correct equation based on the sphere's definition is $x^2 + y^2 + z^2 = r^2$, and the error seems to be in the calculation or interpretation of the radius squared in the question's choices. Given the options, the closest to the expected format is $x^2 + y^2 + z^2 = r^2$, which matches option C if we disregard the discrepancy in the squared radius value provided.

A Spherical Building Has a Diameter Of 201201201 FeetThe Center of the Building Is Placed at the Origin

A Spherical Building Has a Diameter Of $201$ FeetThe Center of the Building Is Placed at the Origin