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

Tutors, sign in to answer this question.

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

(5 rotations)(pi D inches / rotation)(1 foot/12 inches) = 37.94 feet

D = 37.94 * 12 / (5 * 3.14) inches

D = 28.99872611464968 inches = 29 inches

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

37.94ft/ 5 = 7.59 ft

d∏ = 7.59 ft

d = 2.42 ft

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

Final answer = 2.42 feet

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

James P. | Experienced Math TutorExperienced Math Tutor

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**

James G. | Jim the Computer and Math TeacherJim the Computer and Math Teacher

37.94/5 = 7.588 feet = 3.14 * Diameter,

Diameter = 7.588/3.14 * 12 = 28.999, so 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

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.