(a) To determine Calculate the volume of the solid generated by revolving the region about x axis. Explanation Given information: The solid generated by revolving the triangular region with vertices ( 0 , 0 ) , ( b , 0 ) , and ( 0 , h ) . Calculation: Sketch the triangular region with vertices ( 0 , 0 ) , ( b , 0 ) , and ( 0 , h ) as shown in Figure 1. Refer to Figure 1. Provide the equation of line as shown below. y = − h b x + h The outer radius R ( x ) = − h b x + h . The inner radius r ( x ) = 0 . The region lies between 0 to b. Calculate the volume of the solid about x axis using the formula: V = ∫ a b π ( [ R ( x ) ] 2 − [ r ( x ) ] 2 ) d x (1) Substitute − h b x + h for R ( x ) , 0 for r ( x ) , 0 for a , and b for b in Equation (1) (b) To determine Calculate the volume of the solid generated by revolving the region about y axis.

4th Edition

ISBN: 9780134439099

Author: Hass, Joel., Heil, Christopher , WEIR, Maurice D.

Publisher: Pearson,

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 6.1, Problem 52E

(a)

To determine

Calculate the volume of the solid generated by revolving the region about x axis.

(b)

To determine

Calculate the volume of the solid generated by revolving the region about y axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.1, Problem 51E

Chapter 6.1, Problem 53E

Students have asked these similar questions

Don't do 14. Please solve 19

Please solve 14 and 15

1. Consider the following system of equations: x13x2 + 4x3 - 5x4 = 7 -2x13x2 + x3 - 6x4 = 7 x16x213x3 - 21x4 = 28 a) Solve the system. Write your solution in parametric and vector form. b) What is a geometric description of the solution. 7 c) Is v = 7 in the span of the set S= [28. 1 HE 3 -5 3 ·6 ? If it is, write v 6 as a linear combination of the vectors in S. Justify. d) How many solutions are there to the associated homogeneous system for the system above? Justify. e) Let A be the coefficient matrix from the system above. Find the set of all solutions to Ax = 0. f) Is there a solution to Ax=b for all b in R³? Justify.

Chapter 6 Solutions

Thomas' Calculus

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.