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Volume of Revolution

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

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

The ...

Solution Summary

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