Consider the solid obtained by rotating the region bounded by the curve $y=x^2,x=5$ and $y=0$ around $y-$axis.

Set up the integral to find the volume of the solid using a typical disk or washer.

$($A$){\displaystyle \underset{0}{\overset{5}{}}}{x}^{3}dx$

$($B$)2{\displaystyle \underset{0}{\overset{5}{}}}{x}^{3}dx$

$($C$)2{\displaystyle \underset{0}{\overset{25}{}}}{x}^{3}dx$

$($D$){\displaystyle \underset{0}{\overset{25}{}}}(y-25)dy$

$($E$){\displaystyle \underset{0}{\overset{25}{}}}(25-y)dy$

$($F$)$ None of these

Set up the integral to find the volume of the solid using a typical cylindrical shell.

$($A$){\displaystyle \underset{0}{\overset{5}{}}}{x}^{3}dx$

$($B$)2{\displaystyle \underset{0}{\overset{5}{}}}{x}^{3}dx$

$($C$)2{\displaystyle \underset{0}{\overset{25}{}}}{x}^{3}dx$

$($D$){\displaystyle \underset{0}{\overset{25}{}}}(y-25)dy$

$($E$){\displaystyle \underset{0}{\overset{25}{}}}(25-y)dy$

$($F$)$ None of these

Find the exact volume of the solid.

$($A$)312\mathrm{.}5uni{t}^3$

$($B$)\frac{125}{2}uni{t}^3$

$($C$)\frac{625}{2}uni{t}^3$

$($D$)$ None of these

need help with all three