Lesson 22-Surface Sketching Sphere, Cylinder and Quadrics, Slides of Calculus for Engineers

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Lesson 2

Surface Sketching:

Sphere, Cylinder and

Quadrics

OBJECTIVE:

• At the end of the lesson, the student must be able to:
  • Sketch other surfaces like sphere, cylinders and

quadrics in three dimensional system.

Illustrative

Problem

Illustrative

Problem

Examples:

2. Find the equation of a sphere of radius 3 centered at (2, 3, 9). Given : Radius ( r ) = 3 ; C(2, 3, 9) Solution : (x – x 0 ) 2 + (y – y 0 ) 2 + (z – z 0 ) 2 = r (x – 2) 2 + (y – 3) 2 + (z – 9) 2 = 3
3. Describe the surface whose equation is given. x 2 + y 2 + z 2 + 4x + 6y + 10z – 26 = 0 Solution : x 2 + y 2 + z 2 + 4x + 6y + 10z – 26 = 0 (x 2 + 4x)+ (y 2 + 6y)+( z 2 +10z) = 26 (x 2 + 4x + 4)+ (y 2 + 6y + 9)+( z 2 +10z + 25) = 26 + 4 + 9 + 25 (x + 2) 2 + (y + 3) 2 + ( z + 5) 2 = 64 sphere with center C (-2, -3, -5) and r = 8

SURFACES : Cylinder

Illustrative Problem

Illustrative Problem

PARABOLIC CYLINDER

Illustrative

Problem

PARABOLIC CYLINDER

Illustrative

Problem

6. z 2 = y – 1

PARABOLIC CYLINDER

SURFACES : Quadric

Common Types of Quadric Surfaces

1. Ellipsoid

2. Elliptic Paraboloid

3. Elliptic Cone

4. Hyperboloid of One Sheet

5. Hyperboloid of Two Sheets

6. Hyperbolic Paraboloid

QUADRIC SURFACE

nd

Type of Quadric Surface

rd

Type of Quadric Surface