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 :

$\qquad \tt \dashrightarrow \:c = \frac{distance \: covered}{number \: of \: revolutions}$

Now, equate both the equations ~

$\qquad \tt \dashrightarrow \:2 \pi r = \frac{distance \: covered}{number \: of \: revolutions}$

$\qquad \tt \dashrightarrow \:2 \pi r = \frac{65}{13}$

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

$\qquad \tt \dashrightarrow \:r = \frac{5}{2 \pi}$

$\qquad \tt \dashrightarrow \:r = \frac{5}{3.14 \times 2}$

$\qquad \tt \dashrightarrow \:r = \frac{5}{6.28}$

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

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

• radius of wheel is 80 cm

[ To the hundredth place : 0.796 m ]