# Worksheet: Equation of a Sphere

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: **

Does the given 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 .

**Q2: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- AYes, it describes a sphere. Its radius is 1 and its center is at .
- BYes, it describes a sphere. Its radius is 1 and its center is at .
- CYes, it describes a sphere. Its radius is 2 and its center is at .
- DYes, it describes a sphere. Its radius is 2 and its center is at .
- ENo, it does not describe a sphere.

**Q3: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- ANo, it does not describe a sphere.
- BYes, it describes a sphere. Its radius is 1 and its center is at .
- CYes, it describes a sphere. Its radius is 5 and its center is at .
- DYes, it describes a sphere. Its radius is 5 and its center is at .
- EYes, it describes a sphere. Its radius is 1 and its center is at .

**Q4: **

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

- A
- B
- C
- D

**Q6: **

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

- A
- B
- C
- D

**Q7: **

Determine the equation of a sphere with center , given that it touches one of the coordinate planes.

- A
- B
- C
- D

**Q8: **

Given that a sphereβs equation is , determine its center and radius.

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

**Q9: **

A sphere of radius 2 is tangent to all three coordinate planes. Given that the coordinates of its centre are all positive, what is the equation of this sphere?

- A
- B
- C
- D

**Q10: **

Determine the surface area of the sphere of equation , leaving your answer in terms of .

- A
- B
- C
- D

**Q11: **

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

- A
- B
- C
- D

**Q12: **

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

- A
- B
- C
- D

**Q13: **

A sphere is tangent to the -plane, and has its center on the -axis at a distance of 35 length units from the -plane. What is the equation of the sphere?

- A or
- B or
- C or
- D or

**Q14: **

The line is tangent to the sphere . Find the sphereβs radius to the nearest hundredth.

**Q15: **

Which of the following does the equation represent?

- AA circle of radius length units
- BA plane
- CA sphere of radius length units
- DA circle of radius 3 length units
- EA sphere of radius 3 length units

**Q16: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- AYes, it describes a sphere of radius 1 centered at .
- BNo, it does not describe a sphere.
- CYes, it describes a sphere of radius 3 centered at .
- DYes, it describes a sphere of radius 1 centered at .
- EYes, it describes a sphere of radius 2 centered at .

**Q20: **

Given that the spheres and are tangential, determine all possible values of .

- A or
- B or
- C or
- D or

**Q21: **

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

- A
- B
- C
- D

**Q22: **

A sphere of radius 50 is centered on the point on the -axis that is at a distance 17 from the -plane. What is the equation of the sphere?

- A or
- B or
- C or
- D or

**Q23: **

A sphere with center and radius 2 touches the - and -planes. Determine all possible values of and .

- A , or ,
- B , or ,
- C , or ,
- D , or ,

**Q24: **

Given that is a diameter of a sphere whose equation is , and the coordinates of are , determine the coordinates of point .

- A
- B
- C
- D

**Q25: **

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

- A
- B
- C
- D