 6.3.1: Which of the following is a solid of revolution? (a) Sphere (b) Pyr...
 6.3.2: True or false? When the region under a single graph is rotated abou...
 6.3.3: True or false? When the region between two graphs is rotated about ...
 6.3.4: Which of the following integrals expresses the volume obtained by r...
 6.3.5: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.6: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.7: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.8: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.9: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.10: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.11: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.12: In Exercises 512, find the volume of revolution about the xaxis fo...
 6.3.13: In Exercises 13 and 14, R is the shaded region in Figure 11. Which ...
 6.3.14: In Exercises 13 and 14, R is the shaded region in Figure 11. Which ...
 6.3.15: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.16: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.17: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.18: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.19: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.20: In Exercises 1520, (a) sketch the region enclosed by the curves, (b...
 6.3.21: In Exercises 2124, find the volume of the solid obtained by rotatin...
 6.3.22: In Exercises 2124, find the volume of the solid obtained by rotatin...
 6.3.23: In Exercises 2124, find the volume of the solid obtained by rotatin...
 6.3.24: In Exercises 2124, find the volume of the solid obtained by rotatin...
 6.3.25: Rotation of the region in Figure 12 about the yaxis produces a sol...
 6.3.26: Let R be the region enclosed by y = x2 + 2, y = (x 2)2 and the axes...
 6.3.27: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.28: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.29: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.30: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.31: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.32: In Exercises 2732, find the volume of the solid obtained by rotatin...
 6.3.33: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.34: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.35: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.36: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.37: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.38: In Exercises 3338, find the volume of the solid obtained by rotatin...
 6.3.39: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.40: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.41: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.42: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.43: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.44: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.45: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.46: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.47: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.48: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.49: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.50: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.51: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.52: In Exercises 3952, find the volume of the solid obtained by rotatin...
 6.3.53: The bowl in Figure 14(A) is 21 cm high, obtained by rotating the cu...
 6.3.54: The region between the graphs of f and g over [0, 1] is revolved ab...
 6.3.55: Find the volume of the cone obtained by rotating the region under t...
 6.3.56: The torus (doughnutshaped solid) in Figure 15 is obtained by rotat...
 6.3.57: Sketch the hypocycloid x2/3 + y2/3 = 1 and find the volume of the s...
 6.3.58: The solid generated by rotating the region between the branches of ...
 6.3.59: A bead is formed by removing a cylinder of radius r from the center...
 6.3.60: Find the volume V of the bead (Figure 17) in terms of r and R. Then...
 6.3.61: The solid generated by rotating the region inside the ellipse with ...
 6.3.62: The curve y = f (x) in Figure 18, called a tractrix, has the follow...
 6.3.63: Verify the formula x2 x1 (x x1)(x x2)dx = 1 6 (x1 x2) 3 3
 6.3.64: Let R be the region in the unit circle lying above the cut with the...
Solutions for Chapter 6.3: Volumes of Revolution
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 6.3: Volumes of Revolution
Get Full SolutionsChapter 6.3: Volumes of Revolution includes 64 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 64 problems in chapter 6.3: Volumes of Revolution have been answered, more than 41674 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Arccosine function
See Inverse cosine function.

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Domain of a function
The set of all input values for a function

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Event
A subset of a sample space.

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Natural logarithm
A logarithm with base e.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Regression model
An equation found by regression and which can be used to predict unknown values.

Sine
The function y = sin x.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Speed
The magnitude of the velocity vector, given by distance/time.

Statistic
A number that measures a quantitative variable for a sample from a population.

Third quartile
See Quartile.

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.