Question

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

Answer 1

Answer:

$V=339.12\ cm^3$

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

$V=khr^{2}$

where

K is the constant of proportionality

step 1

Find the value of k with the initial values

$V=157.00\ cm^3\\h=2\ cm\\r^2=25\ cm^2$

substitute

$157.00=k(2)(25)$

solve for k

$k=157.00/50\\k=3.14$

so

$V=3.14hr^{2}$

step 2

Find v when h=3 cm and r^2=36 cm^2

substitute in the equation and solve for V

$V=3.14(3)(36)\\V=339.12\ cm^3$