Question

A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel?

27.5 cm2

390.1 cm2

195.1 cm2

97.5 cm2

Answer 1

The amount of distance the wheel rolled is the circumference of that wheel. So we know the circumferenece of the wheel is 35cm; this is important because the formula for finding circumference is
`2 \pi r = C`. We can solve this for radius.


`2 \pi r = 35`

Divide by 2.

`\pi r = 17.5`

Divide by
`\pi`

`r = 5.57`

So we now know the radius of the wheel is 5.57. We can then use this knowledge to find the area of the wheel. The formula for area is
`\pi r^2 = A`


`\pi 5.57^2 = A`

Square 5.57.

`\pi 31.02 = A`

Multiply by
`\pi`

`97.47 = A`

This means the answer is the last one in the list given.