A paddle wheel on a boat is 12 feet in diameter. The fins along the outer edge travel at
a speed of 7.2 feet per second. How long does it take the paddle wheel to complete 100
full revolutions? Round to the nearest second.

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:

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.