Question

"The difference between the circumference and diameter of a wheel is 18cm. Find the radius of the wheel. Use 3.14 for Pi. Round to the nearest tenth."

Answer 1

`4.2\ \text{cm}`

Explanation:

d = Diameter of wheel

The difference between the circumference and diameter of a wheel is 18 cm.

`2\pi r-d=18\\\Rightarrow \pi d-d=18\\\Rightarrow d(\pi-1)=18\\\Rightarrow d=(18)/(\pi -1)\\\Rightarrow d=(18)/(3.14-1)\\\Rightarrow d=8.41\ \text{cm}`

The diameter of the wheel is 8.41 cm so the radius will be
`(8.41)/(2)=4.205\approx 4.2\ \text{cm}`.