The problem is asking for the height of the fluid using the following information:
Volume of fluid
=
V
=
36
π
cm
3
Radius of new cylinder
=
r
=
3
cm
To start the solution, solve for the height
h
in the formula for the volume of a cylinder:
V
=
π
r
2
h
π
r
2
h
π
r
2
=
V
π
r
2
h
=
V
π
r
2
V =π
r
2
h
π
r
2
h
π
r
2
=
V
π
r
2
h =
V
π
r
2
Substituting the values of the volume and the radius, the height of the fluid is:
h
=
V
π
r
2
=
36
π
cm
3
(
3
cm
)
2
=
(
4
)
(
9
)
π
cm
3
(
9
)
cm
2
=
4
π
cm
=
12.5663706144
≈
12.6
cm
h =
V
π
r
2
=
36
π
cm
3
(
3
cm
)
2
=
(
4
)
(
9
)
π
cm
3
(
9
)
cm
2
=4π cm =12.5663706144≈12.6 cm
Thus, the fluid reaches up to
12.6
cm
12.6
cm
in the new cylinder.
The answer would be Y= -2x-7 if im not mistaken because the slope of the equation is 1/2 and to find the perpendicular equation you take the negative reciprocal so that would make the slope -2 and I believe the y intercept would be -7 if it must go through the point (-8,2)