Answer:
[tex]V=339.12\ cm^3[/tex]
Step-by-step explanation:
we know that
If the volume of a cylinder varies jointly with the height h and the radius squared
we have
[tex]V=khr^{2}[/tex]
where
K is the constant of proportionality
step 1
Find the value of k with the initial values
[tex]V=157.00\ cm^3\\h=2\ cm\\r^2=25\ cm^2[/tex]
substitute
[tex]157.00=k(2)(25)[/tex]
solve for k
[tex]k=157.00/50\\k=3.14[/tex]
so
[tex]V=3.14hr^{2}[/tex]
step 2
Find v when h=3 cm and r^2=36 cm^2
substitute in the equation and solve for V
[tex]V=3.14(3)(36)\\V=339.12\ cm^3[/tex]