Question

1) A cylinder has a volume of 20 cubic feet. What is that volume in cubic inches? (1 ft = 12 in) ​

Answer 1

Before calculating the volume of this cylinder, we must either convert the diameter to feet or the height to inches. I'll do the latter, to avoid getting a very small number.
Recall that there are
12
inches in
1
foot. Thus, we can state:
12
in.
1
ft.
=
x
4
ft.
x
=
12
in.
×
4
ft.
1
(ft.)
x
=
48
in.
Hence, the cylinder has a height of
48
inches.
Now, we can apply the formula for volume of a cylinder to effectuate our calculation. The formula in question is
V
=
a
base
×
h
, or
V
=
r
2
π
×
h
.
However, we know our diameter but we don't know our radius. As you probably know, the diameter is linked to the radius b the formula
d
=
2
r
. Solving for
r
and substituting:
r
=
d
2
r
=
12
2
r
=
6
∴
The radius of the cylinder measures
6
inches.
V
=
r
2
π
×
h
V
=
6
2
π
×
48
V
=
(
36
×
48
)
π
V
=
1728
π
in
2
Note that this answer is in exact value. Rounded to two decimal places, the volume is
5428.67
in