# Question 3755d

Mar 25, 2017

$V = 1024 \frac{\pi}{3}$

$V \approx 1072.3$

#### Explanation:

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:

$f \left(x\right) = - \sqrt{64 - {x}^{2}}$

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

The disk method says

$V = \pi {\int}_{a}^{b} {\left(f \left(x\right)\right)}^{2} \mathrm{dx}$

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

$V = \pi {\int}_{0}^{8} {\left(- \sqrt{64 - {x}^{2}}\right)}^{2} \mathrm{dx}$

$V = \pi {\int}_{0}^{8} \left(64 - {x}^{2}\right) \mathrm{dx}$

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

$V = 1024 \frac{\pi}{3}$

$V \approx 1072.3$