# Lesson Worksheet: Equation of a Sphere Mathematics

In this worksheet, we will practice finding the equation of a sphere given its center and finding the center and the radius given the sphere’s equation.

Q1:

Give the equation of the sphere of center and radius 3 in standard form.

• A
• B
• C
• D

Q2:

Which of the following is the equation of the sphere of center and passing through ?

• A
• B
• C
• D

Q3:

Find the equation of the sphere with and as endpoints of a diameter.

• A
• B
• C
• D

Q4:

Give the equation of the sphere of center that touches the -plane.

• A
• B
• C
• D

Q5:

Find the equation of a sphere that passes through the points and , given that its center lies on the -axis.

• A
• B
• C
• D

Q6:

Given that a sphere’s equation is , determine its center and radius.

• A, 289 length units
• B, 17 length units
• C, 17 length units
• D, 289 length units

Q7:

Given , and that is a diameter of the sphere , what is the point ?

• A
• B
• C
• D

Q8:

Give the center and radius of the sphere .

• A
• B
• C
• D

Q9:

Does the equation describe a sphere? If so, find its radius and center.

• AYes, it describes a sphere. Its radius is 11 and its center is at .
• BYes, it describes a sphere. Its radius is 11 and its center is at .
• CNo, it does not describe a sphere.
• DYes, it describes a sphere. Its radius is 5 and its center is at .
• EYes, it describes a sphere. Its radius is 5 and its center is at .

Q10:

Find the equation of the sphere concentric with , but with twice the radius.

• A
• B
• C
• D

This lesson includes 26 additional questions and 234 additional question variations for subscribers.