Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Round your answer to two decimal places.
A) 674.33
B) 17.75
C) 96.05
D) 301.76
E) 453.96

Question

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations  about the x-axis. Round your answer to two decimal places.
A) 674.33 
B) 17.75 
C) 96.05 
D) 301.76 
E) 453.96

Quizplus · Accepted Answer

We can use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 
The region bounded by the graphs is a trapezoidal shape, with a larger base of length 4 and a smaller base of length 2, and a height of 3.

Using the shell method, we integrate from x=0 to x=2. The radius of each cylindrical shell is x, and the height is y=4-x^2. Thus, the volume of each cylindrical shell is:

V = 2πx(4-x^2) dx

Integrating from x=0 to x=2, we have:

V = ∫[0,2] 2πx(4-x^2) dx
V = 2π∫[0,2] (4x-x^3) dx
V = 2π [(2x^2) - (1/4)x^4] [0,2]
V = 2π [(2(2)^2) - (1/4)(2)^4] - 0
V = 301.76

Therefore, the answer is D) 301.76.

Use the Disk or the Shell Method to Find the Volume