onsider the solid obtained by rotating the region bounded by the given curves about the y-axis. y = x^2/16 text(, ) x = 2 text(, ) y = 0 Find the volume V of this solid.
Accepted Solution
A:
Answer:The volume of solid will be [tex]\dfrac{\pi}{2}[/tex] cubic unitStep-by-step explanation:Given: The given curves [tex]y=\dfrac{x^2}{16}[/tex]Rotation about y-axis to form a solid bounded by given curve, x=2 and y=0. Please see the attachment for figure. Volume of solid rotation about y-axis using cylindrical shell method. [tex]V=\int_a^b2\pi rhdx[/tex]where, a is lower limit (a=0)b is upper limit (b=2)r is radius (r=x)h is height ([tex]h=y=\dfrac{x^2}{16}[/tex])using the above formula the volume of solid we get [tex]V=\int_0^22\pi\cdot\dfrac{x^3}{16}dx[/tex][tex]V=2\pi\cdot\dfrac{x^4}{64}|_0^2[/tex][tex]V=\dfrac{\pi}{2}[/tex]Hence, The volume of solid will be [tex]\dfrac{\pi}{2}[/tex]