The volume of the solid obtained by revolving the region between the lines and about the y-axis is
A) .
B) .
C) .
D) .
E) .

Question

The volume of the solid obtained by revolving the region between the lines  and  about the y-axis is 
A) . 
B) . 
C) . 
D) . 
E) .

Quizplus · Accepted Answer

The region between the two lines can be represented by the function $f(x)=\frac{x-1}{2}$ and $g(x)=-\frac{x}{3}+3$. To find the bounds of the integral, we set the two functions equal to each other and solve for x: $$\frac{x-1}{2}=-\frac{x}{3}+3$$ $$x=2.2$$ To calculate the volume of the solid, we use the formula: $$V=\pi\int_{0}^{2.2}(\frac{x-1}{2})^2-(-\frac{x}{3}+3)^2 dx$$ This integral evaluates to $\frac{726\pi}{25} \approx 90.75$. Therefore, the correct answer is B (11eaa655_3b22_aaf1_a696_b7b091bf52a4_TB5596_11), which is closest to 90.75.

The Volume of the Solid Obtained by Revolving the Region