Question

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. X = 5 sqrt( y) text(, ) x = 0 text(, ) y = 4 Find the volume V of this solid. V

Answer 1

Answer:

V = 200 π

Step-by-step explanation:

x = 5√y ,   x = 0 ,   y = 4

Determine the volume of the solid V

when x = 0  y = 0

we can calculate the volume of the solid by applying the washer method

V = π ₀⁴∫ [ 0 + ( 5√y )^2 ]  dy

   = π ₀⁴∫ [ 0 + ( 25(y) ) ]  dy

V  = π [ 0 + 25/2 ( y^2 ) ] ⁴₀

V = π [ 25/2 ( 16 ) ]

  = 200 π