Question

Volume of cylinders, spheres, and cones word problems

A graduated cylinder is filled with 367 cm3 of liquid. The liquid is poured into a different cylinder that has a
radius of 3 cm.
What will the height of the liquid be in the new cylinder?
cm

Answer 1

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.