Question #3755d

Question

1492 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-25T03:52:24

$V = 1024pi/3$

$V~~1072.3$

Use the disk method , because it is easy to obtain a function that describes a side view slice of the lower half of the bowl:

$f(x) = -sqrt(64-x^2)$

graph{-sqrt(62-x^2) [-9, 9, -9, 2]}

The disk method says

$V = piint_a^b(f(x))^2dx$

Because we only want the side view of the right half of the curve, we are going from $x = 0$ to $x = 8$

$V = piint_0^8(-sqrt(64-x^2))^2dx$

$V = piint_0^8(64-x^2)dx$

$V = pi(64x-x^3/3|_0^8$

$V = 1024pi/3$

$V~~1072.3$