The length of the smaller and bigger hands of a watch are 3.5 cm and 4.2 cm long. The distances traced by their tips from 7:00 am to 7:15 am bear the ratio:
Answers
Given : The length of the smaller and bigger hands of a watch are 3.5 cm and 4.2 cm long.
To Find : The distances traced by their tips from 7:00 am to 7:15 am bear the ratio:
Solution:
Distance covered by Tip = (angle covered/ 360°) 2π(Radius)
Distance covered ∝ Radius if angle is fixed
As time for both is 7:00 am to 7:15 hence angle is same for both
Hence ratio of Distance covered = Ratio of their radius
=> Ratio = 3.5 : 4.2
=> Ratio = 5 : 6
The distances traced by their tips from 7:00 am to 7:15 am bear the ratio:
5 : 6
Learn More:
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Step-by-step explanation:
we have to find the arc made by their tips as given in the question,
smaller
angle made by small hand=360°=12hr completed by small hand then
angle made by it in 15 min
so, 12hr=720min=360°
15min=360°/720°*15=15/2
now,distance(arc)=theta/360°*πr²
=15/2*1/360*2*22/7*3.5
=55/120cm
second hand
minute hand
360°=60min
in 15min=360/60*15=90°
now distance (arc)=90/360*2*22/7*4.2
=66/10cm
now ratio=55/120*10/66=5/72