Answer:
Explanation:
First, we must determine the circumference of the paddle wheel.
The formula for the circumference of a circle is:
c
=
2
π
r
Where
r
is the radius of the circle.
However, we know
d
=
2
r
where
d
is the diameter of the circle.
Therefore:
c
=
2
r
π
=
d
π
Substituting
12
ft
for
d
gives a circumference of:
c
=
12
π
ft
The time it takes to complete 1 revolution can be found using the formula:
t
=
d
s
Where:
t
is the time it takes: what we are solving for in this problem.
d
is the distance traveled: we calculated this as
12
π
ft
s
is the speed traveled: from the problem we know this is
7.2
ft
sec
Substituting and calculating
t
gives:
t
=
12
π
ft
7.2
ft
sec
t
=
12
π
ft
sec
7.2
ft
t
=
12
π
ft
sec
7.2
ft
t
=
12
π
sec
7.2
t
=
1
.
¯
6
π
sec
Two find how long it would take for 100 revolutions we can multiply this time by
100
100
×
1
.
¯
6
π
sec
⇒
166
.
¯
6
π
sec
If a number is required for the answer we can use 3.14 as an estimate for
π
giving:
166
.
¯
6
π
sec
⇒
166
.
¯
6
×
3.14
sec
⇒
523
sec
Step-by-step explanation:
