Assuming you made a decent sketch,
x = (y-9)^2
± √x = y - 9
y = 9 + √x and y = 9 - √x
notice the parabola has vertex at (0,9) and it intersects x = 16
and y = 5 at (16,5)
upper height above y = 5 is y = 9+√x - 5 = 4 + √x <---- larger radius
lower height above y = 5 is y = 9-√x - 5 = 4 - √x <----- smaller radius
volume = π∫ ( (4+√x)^2 - (4 - √x)^2 ) dx from 0 to 16
= π ∫ 16√x dx from 0 to 16
= π [ 32/3 x^(3/2) ] from 0 to 16
= π ( (32/3)(64) - 0 )
= 2048/3 π
better check my steps, my 82 year old brain ain't what it used to be.
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
x = (y − 9)^2, x = 16; about y = 5
1 answer