Question #3755d

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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#