I assume the axis of rotation is the line y=49. So, the shells have thickness dy, and
v = ∫[0,49] 2πrh dy
where r = 49-y and h = (7+√(49-y))-(7-√(49-y))
v = ∫[0,49] 2π(49-y)((7+√(49-y))-(7-√(49-y))) dy = 26891.2π
you can check using discs:
v = ∫[0,14] π(R^2-r^2) dx
where R=49 and r=49-y
v = ∫[0,14] π(49^2-(49-(14x-x^2))^2) dx
Use the shell method
y=14x-x^2, x=0, y=49
1 answer
1 answer