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.

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.

... Please see the attached file. Several volumes of solids of revolution are calculated, and the general formula for the volume of such a solid is derived. ...

... Use cylindrical shells to compute the volume of the region bounded by and x ... up the integral for the surface area of the surface of revolution, and approximate ...

... total angular distance traveled over the 90 s time interval, expressed in both radians and revolutions? 1) A sphere has a radius 1.500m Find its volume in cm^3 ...

... In the following posting, volumes of solids of revolution are found using ... For the following problem, sketch the region and then find the volume of the ...

Volume of a Solid of Revolution by Shell Method. ... f) Write a formula for the volume of the typical shell. ... sum that corresponds to adding up the volumes of n such ...

... edu/visual.calculus/5/volumes.5/ http://en.wikipedia.org/wiki/Solid_of_revolution. Hopr this helps Thanks again Yinon. A volume of solid of revolution is found. ...

Volume of a Solid of Revolution Region. ... The volume of a solid of revolution is found in an attached Word document. This detailed solution includes a diagram. ...