Explore BrainMass

Explore BrainMass

    Volume of Revolution

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddf
    https://brainmass.com/math/integrals/12850

    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 Summary

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

    $2.49

    ADVERTISEMENT