Question

PLEASE HELP ASAP THANK YOUU: A unicycle wheel makes five rotations. The unicycle travels 37.94 feet. Find the diameter of the wheel in inches.

Show your work and write your answer in a sentence.

Answer 1

diameter of the wheel = 28.98 in (2 d.p.)

Explanation:

Given information:

• A unicycle wheel makes five rotations
• The unicycle travels 37.94 feet

Circumference of a circle = πd (where d is the diameter)

One rotation of the wheel is equal to the circumference of the wheel.

Therefore, 5 rotations is equal to the sum of 5 circumferences.

To find the diameter of the wheel in feet, equate the expression for 5 circumferences to the total distance traveled and solve for d:

`\begin{aligned}\textsf{5 circumferences} & = \textsf{total distance traveled}\\\implies 5 \pi d & = \sf 37.94\: ft\\d & = \sf (37.94)/(5 \pi)\\d & = \sf 2.415335416... \:ft \end{aligned}`

As 1 foot = 12 inches, multiply the found diameter in feet by 12 to calculate the diameter in inches:

`\begin{aligned}d & =2.415335416... * 12\\\implies d & = \sf 28.98\:\:in\:(2\:d.p.)\end{aligned}`

Therefore, the diameter of the wheel is 28.98 in (2 d.p.).