Question

A wheel makes 13 revolutions to cover a distance of 65 m. Find the radius of the wheel.

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Circumference of the wheel is :

`\qquad \tt \dashrightarrow \:c = 2 \pi r`

• c = circumference

• r = radius

Number of revolutions = 13, and distance travelled is 65 m.

So, we can infer that :

`\qquad \tt \dashrightarrow \:c = (distance \: covered)/(number \: of \: revolutions)`

Now, equate both the equations ~

`\qquad \tt \dashrightarrow \:2 \pi r = (distance \: covered)/(number \: of \: revolutions)`

`\qquad \tt \dashrightarrow \:2 \pi r = (65)/(13)`

`\qquad \tt \dashrightarrow \:2 \pi r = 5`

`\qquad \tt \dashrightarrow \:r = (5)/(2 \pi)`

`\qquad \tt \dashrightarrow \:r = (5)/(3.14 * 2)`

`\qquad \tt \dashrightarrow \:r = (5)/(6.28)`

`\qquad \tt \dashrightarrow \:r \approx0.8 \: m`

`\qquad \tt \dashrightarrow \:r \approx80 \: cm`

• radius of wheel is 80 cm

[ To the hundredth place : 0.796 m ]