I think its 44 too,but what do i know
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Find attached the graph and a table with some important points.
Note that every point of the graph is the extreme of a vector whose radius is r and angle is theta.
The answer is 243
hope this helps
The answer to the questions of volumes are given as follows
a) 
b) 
c)
d)
Generally, the questions are mathematically solved below

a) x-axis
if $y=4, x=16, x=0$
Using disk method




b) line y=4
if x=0, y=0 ;

Using shell method


![v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\](https://tex.z-dn.net/?f=v%3D2%20%5Cpi%5Cleft%5B%5Cfrac%7B4%20y%5E%7B3%7D%7D%7B3%7D-%5Cfrac%7By%5E%7B4%7D%7D%7B4%7D%5Cright%5D_%7B0%7D%5E%7B4%7D%20%5C%5C)
![v=\frac{2 \pi}{12}[1024-768] \\](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B2%20%5Cpi%7D%7B12%7D%5B1024-768%5D%20%5C%5C)


c) y-axis
0 ≤ y ≤ 4
x=y^2
Using disk method
volume



d) line x=-1
y=√x, y=4, x=0
0 ≤ x ≤ 6
Using shell method
volume is


![V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\](https://tex.z-dn.net/?f=V%3D2%20%5Cpi%5Cleft%5B%5Cfrac%7Bx%5E%7B3%20%2F%202%7D%7D%7B3%20%2F%202%7D%2B%5Cfrac%7Bx%5E%7B5%20%2F%202%7D%7D%7B5%20%2F%202%7D%5Cright%5D_%7B0%7D%5E%7B16%7D%20%5C%5C)
![V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\](https://tex.z-dn.net/?f=V%3D2%20%5Cpi%5Cleft%5B2%20%2F%203%20%5Ccdot%5Cleft%284%5E%7B2%7D%5Cright%29%5E%7B3%20%2F%202%7D%2B2%20%2F%205%5Cleft%284%5E%7B2%7D%5Cright%29%5E%7B5%20%2F%202%7D%5Cright%5D%20%5C%5C)





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