The line segment x = 1 - y, 0 ≤ y ≤ 1, is revolved about the y-axis to generate the cone in Figure 6.49. Find its lateral surface area (which excludes the base area). A (0, 1) x+y=1 B (1,0) FIGURE 6.49 Revolving line segment AB about the y-axis generates a cone whose lateral surface area we can now calculate O dx 2 ° S = 2x [^*^ √/ 1 + ( 1 ² ³ dy = 2x / ² (1 S X, 1+ dy 0 (1-y)√2y dy 1 dx 2 S = 2x [*^ √ 1 + = =+) ² dy = 2 = [" (1-3)√2dy S dy 0 dx S = 27 / ²x √/1 + (# ) ² dy = 27 / ² (1+ dy 0 dy=2л (1+y) √2dy O dx S=2x [ ^x√/1+ (#5) ³ dy=25 / ^ (1-y) √ydy dy 0 dx ° 2020 ["^ √/10 (2) 4-2 [ " (2-31 / 54 S = 2n x,/ 1+ dx=2r √ 2dx dy 0

The line segment x = 1 - y, 0 ≤ y ≤ 1, is revolved about the y-axis to generate the cone in Figure 6.49. Find its lateral surface area (which excludes the base area). A (0, 1) x+y=1 B (1,0) FIGURE 6.49 Revolving line segment AB about the y-axis generates a cone whose lateral surface area we can now calculate O dx 2 ° S = 2x [^^ √/ 1 + ( 1 ² ³ dy = 2x / ² (1 S X, 1+ dy 0 (1-y)√2y dy 1 dx 2 S = 2x [^ √ 1 + = =+) ² dy = 2 = [" (1-3)√2dy S dy 0 dx S = 27 / ²x √/1 + (# ) ² dy = 27 / ² (1+ dy 0 dy=2л (1+y) √2dy O dx S=2x [ ^x√/1+ (#5) ³ dy=25 / ^ (1-y) √ydy dy 0 dx ° 2020 ["^ √/10 (2) 4-2 [ " (2-31 / 54 S = 2n x,/ 1+ dx=2r √ 2dx dy 0

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section: Chapter Questions

Problem 3CR

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