Question

The lengths of smaller and bigger hands of watch are 3.50 cm and 4.62 cm respectively. Find the ratio of distances transversed from 6 am to 6 pm ​

Answer 1

The distance traversed can be calculated using the perimeter formula of circle.

Let Pb = Perimeter of by Bigger Hand

Ps = Perimeter by Minute Hand

Db = Distance traversed by Bigger Hand

Ds = Distance traversed by Smaller Hand

Pb = 2 × π × 4.62

Ps = 2 × π × 3.5

Distance traversed in 12 hours

Distance Bigger = Pb × 12

Distance Smaller = Ps × 12

Ratio

Db : Ds = 4.62 : 3.5

Since, all other figures get cancelled in the division, the lengths of the hands remain there.

We can rewrite the ratio as

Ratio Db : Ds = 1.32 : 1

or

Db : Ds = 132 : 100