__Applications of Pi__

## Application #1

We are going to show how using the circumference of a bike tire is helpful to find out how far a person has traveled on his or her bike. We are going to have to find the circumference of the wheel first.

Suppose the radius of the wheel is 31cm, so using the formula 2πr the circumference of the wheel is approximately 194.78 cm.

Let’s say, we have been biking for 20 minutes and we know that our wheels have made 5000 revolutions and we want to know how far we’ve traveled.

To do so, we can multiply the number of revolutions by the circumference of the wheel to get the distance traveled.

In this case it would be 5000 times 194.78 cm which equals 973900 cm or 9.739 km, so we know we've traveled approximately 9.739 km.

This concept can be used in any device that measures the distance traveled by an object on wheels, such as an odometer for cars or bikes, by simply multiplying the number of revolutions the wheels have made (which a computerized device can easily count) by the circumference of the wheel.

Suppose the radius of the wheel is 31cm, so using the formula 2πr the circumference of the wheel is approximately 194.78 cm.

Let’s say, we have been biking for 20 minutes and we know that our wheels have made 5000 revolutions and we want to know how far we’ve traveled.

To do so, we can multiply the number of revolutions by the circumference of the wheel to get the distance traveled.

In this case it would be 5000 times 194.78 cm which equals 973900 cm or 9.739 km, so we know we've traveled approximately 9.739 km.

This concept can be used in any device that measures the distance traveled by an object on wheels, such as an odometer for cars or bikes, by simply multiplying the number of revolutions the wheels have made (which a computerized device can easily count) by the circumference of the wheel.

Application #2

Suppose we have a completely filled cylindrical can of paint without a label and we want to know how much paint is in the can.

Let’s say we measure the height of the can and it is 10 cm.

Let’s also say we measure the diameter of the can and it is 6 cm.

The formula for figuring out the volume (V) of the can is: area of the base of the can times the height (h) of the can, which can be written as V = (πr

Using this formula we can figure out how much paint is in the can.

Since the radius (r) is half the diameter, the radius is 3 cm (half of 6 cm).

So now we can do the equation πr

The next step is to multiply 9π cm

This equation is approximately equal to 282.7 cm

Let’s say we measure the height of the can and it is 10 cm.

Let’s also say we measure the diameter of the can and it is 6 cm.

The formula for figuring out the volume (V) of the can is: area of the base of the can times the height (h) of the can, which can be written as V = (πr

^{2})h.Using this formula we can figure out how much paint is in the can.

Since the radius (r) is half the diameter, the radius is 3 cm (half of 6 cm).

So now we can do the equation πr

^{2}which is equal to 9π cm^{2}.The next step is to multiply 9π cm

^{2}by the height which is 10 cm.This equation is approximately equal to 282.7 cm

^{3}which is equal to 282.7 mL which is approximately how much paint that would be in the can.