Question

Determine the volume of the solid formed when the region enclosed by the curve y=√x, the x-axis and the linex= 4, is revolved about the line x= 4.

Answer 1

Using shell method, the volume of the solid of the revolution is:

$V = \int_0^4 2 \pi \cdot (4-x) \sqrt{x} dx = 2 \pi (\frac{8}{3}x^{3/2} - \frac{2}{5}x^{5/2})|_0^4 = \frac{256}{15}\pi$.