Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { x },$ the x-axis, $x = 4;$ about the x-axis. Then V is

A) $8 \pi$
B) $7 \pi$
C) $6 \pi$
D) $5 \pi$
E) $4 \pi$

Question

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { x },$ the x-axis, $x = 4;$ about the x-axis. Then V is

A) $8 \pi$
B) $7 \pi$
C) $6 \pi$
D) $5 \pi$
E) $4 \pi$

Quizplus · Accepted Answer

The volume of the solid generated by revolving the region enclosed by $y = \sqrt{x}$, the x-axis, and $x = 4$ about the x-axis can be found using the disk method. The formula for the volume is $\int_{a}^{b} \pi [f(x)]^2 dx$, where $f(x) = \sqrt{x}$, $a = 0$, and $b = 4$. Substituting these values into the formula gives $\int_{0}^{4} \pi x dx = \frac{1}{2} \pi x^2 \Big|_0^4 = 8\pi$.

Let V Be the Volume of the Solid Generated by Revolving