Purchase Solution

Volume of Revolution

Not what you're looking for?

Ask Custom Question

1. The shaded region R, is bounded by the graph of y = x^2 and the line y = 4.

a) Find the area of R.

b) Find the volume of the solid generated by revolving R about the x-axis.

c) There exists a number k, k>4, such that when R is revolved about the line y = k, the resulting solid has the same volume as the solid in part b). Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.

Purchase this Solution

Solution Summary

The volume of revolution of an area bounded by two functions is found.

Solution Preview

a.)
y = x^2 => dy = 2*x*dx
area of R (A) = 2*integration(0 to 4) [x*dy]
=> A = 2*integration(0 to 4)[x*2*x*dx]
=> A = 4*[x^3/3] (0 to 4)
=> A = 4*4^3/3 = 256/3 square unit --Answer

b.)
The ...

Solution provided by:
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts