Geometry Question

Question

Item 10
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

Answer 1

paddle wheel circumference = pi x diameter = 37.7143 feet

total distance traveled = 100 revolutions x circumference = 100 x 37.7143 = 3,771.43 feet

time = distance / speed = 3771.43 / 7.2 = 523.81 seconds = 8.73 minutes

Answer 2

First, we need to find the distance traveled. Lastly, we will divide that by the speed, to find the time.

 

A full revolution = 2 pi

Diameter (D) = 12 feet  => Radius (r) = 6 feet

The perimeter of a circle = pi * D or 2 * pi * r = 12 * pi (feet)

So, 100 revolutions = 100 * 12 * pi = 1200 * pi (feet) (you can find the exact number)

 

Knowing the distance now, we can find the time = 1200 * pi / 7.2 ft/s = (166.67 * pi) seconds

 

Find the exact number and round to the nearest second.