Understanding the Equation of a Sphere

The video tutorial explains how to write the equation of a sphere given its center and radius. It starts by introducing the general form of a sphere's equation and then demonstrates how to substitute the given center coordinates and radius into this equation. The tutorial further simplifies the equation and presents the final form. It concludes by showing the graph of the sphere and highlighting the center point.

What is the center of the sphere mentioned in the problem?

• (4, 3, 1)

• (4, -3, 1)

• (4, -3, -1)

• (3, -4, 1)

What is the radius of the sphere?

• 4

• 5

• 6

• 3

In the general equation of a sphere, what does 'r' represent?

• The volume of the sphere

• The circumference of the sphere

• The radius of the sphere

• The diameter of the sphere

What is the value of 'a' in the equation after substitution?

• 3

• 4

• 5

• 6

How is the term (y - (-3)) simplified in the equation?

• y - 1

• y - 3

• y + 1

• y + 3

What is the simplified form of the equation of the sphere?

• (x - 4)^2 + (y + 3)^2 + (z + 1)^2 = 25

• (x + 4)^2 + (y - 3)^2 + (z - 1)^2 = 25

• (x - 4)^2 + (y - 3)^2 + (z - 1)^2 = 25

• (x + 4)^2 + (y + 3)^2 + (z + 1)^2 = 25

What is the significance of the point (4, -3, -1) in the graph of the sphere?

• It is the intersection with the x-axis

• It is the center of the sphere

• It is a point on the surface of the sphere

• It is the farthest point from the center

What is the equation of the sphere's radius squared?

• 25

• 20

• 15

• 10