Use cylindrical shells to find the volume of the solid when the region enclosed by , x = 1, x = 4, y = 0 is revolved about the y-axis.
A) 0.073 $\pi$
B) 1.000 $\pi$
C) 0.938 $\pi$
D) 0.469 $\pi$
E) 0.656 $\pi$

Question

Use cylindrical shells to find the volume of the solid when the region enclosed by  , x = 1, x = 4, y = 0 is revolved about the y-axis.
A) 0.073 $\pi$ 
B) 1.000 $\pi$ 
C) 0.938 $\pi$ 
D) 0.469 $\pi$ 
E) 0.656 $\pi$

Quizplus · Accepted Answer

We use the formula $V=\int_{a}^{b}2\pi x\cdot f(x)dx$ where $f(x)$ is the distance from the curve to the axis of revolution to find the volume of the solid of revolution. In this case, the axis of revolution is the y-axis so our function will be $f(x)=x$. 
Our bounds are $a=1$, $b=4$. Thus, we have:
\begin{align*}
V &= \int_{1}^{4} 2\pi x \cdot x dx \
&= 2\pi\int_{1}^{4} x^2 dx \
&= 2\pi\cdot\frac{1}{3}(4^3-1^3) \
&= 0.938\pi \
\end{align*}
Therefore, the answer is $\boxed{	extbf{(C)}}$.

Use Cylindrical Shells to Find the Volume of the Solid π\piπ

Use Cylindrical Shells to Find the Volume of the Solid $\pi$