The volume of a cylinder varies jointly with the height h and the radius squared r^2, and v=157.00cm^3 when h=2cm and r^2=25cm^2. Find v when h=3cm and r^2=36cm^2. Round your anwser to the nearest hundreth

Respuesta :

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]

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