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# a bicycle wheel rotate 5 times. the bicycle travels 37.94 feet in inches what is the diameter. using 3.14 for pie

a bicycle wheel rotates 5 times. The bicycle travels 37.94 feet in inches what is the  diameter. Using 3.14 for pie.

Hi Ximena;
(37.94 feet)/(5 rotations)=7.588 feet
7.588 feet is the perimeter of the tire.
perimeter=(diameter)(3.14)
(7.588 feet)[(12 inch)/(1 foot)]=(diameter)(3.14)
The unit of feet/foot is in the numerator and denominator.  It cancels...
(7.588 feet)[(12 inch)/(1 foot)]=(diameter)(3.14)
(7.588)(12 inch)=(diameter)(3.14)
91.056 inches=(diameter)(3.14)
Divide both sides by 3.14...
(91.056 inches)/(3.14)=[(diameter)(3.14)]/(3.14)
29. inches=diameter

If the bicycle wheel rotates 5 times and travels 37.94 feet, then we know that the circumference of the wheel (the outside of the wheel as it touches the ground 5 times around) is 37.94/5 = 7.588

Then we use the formula for the circumference of a circle: 2(pi)(radius) = circumference

We plug in what we know 2(3.14)(radius) = 7.588 and then solve for the radius

We divide 2 from both sides of the equation (3.14)(radius) = 3.794

We divide pi from both sides (radius) = 1.208

Then the last step, we multiply the radius by 2, because we need the diameter, which is double the radius

1.208 * 2 = 2.416 or 2.42 rounded up

The distance traveled in one rotation of the wheel is equal to the circumference, pi*diameter.  So, after five rotations, the distance is 5*3.14*diameter= 37 feet = 444 inches; tre diameter is 444 inches/(5*3.14) =
28.2 inches
Hi Ximena,

First there are two relationships/equations needed in this problem. N is 5 (#of cycles)

1) C=π*D
where C is the circumference
π is pi (3.14)
D is diameter of the wheel

2) L=N*C
where L is the length traveled
N is the number of cycles
C is the circumference

So the problem asks us to find the diameter of the wheel in inches.

L=37.94ft
=37.94 ft * (12in/1ft)
=455.28 inches

take equation (1) and (2) and combine them

L=5*C-->
L=5*(π*D)
substitute 455.28 for L and 3.14 for π...

455.28=5*3.14*D

Solve for D...

455.28/(5*3.14)=D

D=28.998 inches --> D= 29 inches
Distance traveled by wheel in one rotation - circumference of the wheel - 2 x pi x radius = 2 x 3.14 x r

Distance traveled in five times rotation = 5 x 2 x 3.14 x r = 37.94

divide both sides by 5, 2 and 3.14

r = 37.94/(5 x 2 x 3.14) = 1.2 feet = 14.5 inches