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The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days. (Take π = 22/7) - Mathematics

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Sum

The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days. (Take π = 22/7)

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Solution

In 2 days, the short hand will complete 4 rounds.

∴ Distance moved by its tip = 4 (Circumference of a circle of radius 4 cm)

`=4\times ( 2\times \frac{22}{7}\times 4)=\frac{704}{7}\text{ cm}`

In 2 days, the long hand will complete 48 rounds.

∴ Distance moved by its tip

= 48 (Circumference of a circle of radius 6 cm)

`=48\times ( 2\times \frac{22}{7}\times 4 )=\frac{12672}{7}\text{ cm}`

Hence,

Sum of the distance moved by the tips of two hands of the clock

`=( \frac{704}{7}+\frac{12672}{7})=1910.57`

Concept: Circumference of a Circle
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