Question

$\sf\pink{Maths\:Legends\:R\:u\: there...!?}$

● The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distance travelled by their tips in 2 days.

Class - 10th

CBSE - 2018

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Step by step explanation please ​

Answer 1

Things to know

The figure that each tip of the hands draws is a circle. The formula for the circumference is $2\pi r$, where $\pi$ is pi and $r$ is the radius.

Solution

The tip of the short hand moves $8\pi$ cm each revolution, while it revolves once each 12 hours.

The tip of the long hand moves $12\pi$ cm each revolution, while the long hand revolves once each hour.

2 days are given to revolve. Hence, 48 hours are given.

The short hand revolves 4 times, so the distance it travels is

$\rightarrow 32\pi$ cm

The long hand revolves 48 times, so the distance it travels is

$\rightarrow 576\pi$ cm

The sum of the distance traveled is

$\rightarrow \boxed{608\pi}$ cm

Answer 2

Answer:

Given :-

• The short and long hands of a clock are 4 cm and 6 cm respectively.

To Find :-

• What is the sum of distance travelled by their tips in 2 days.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Circumference\: of\: Circle =\: 2{\pi}r}}}$

where,

• r = Radius

Solution :-

$\mapsto$ First, short hand it complete 1 revolution in 12 hours :

Given :

• Radius = 4 cm

And, in 2 days or 48 hours distance travelled then,

$\implies \sf 2 \times \dfrac{22}{7} \times 4 \times 4$

$\implies \sf \dfrac{44}{7} \times 16$

$\implies \sf \dfrac{176}{7}$

$\implies \sf \dfrac{\cancel{704}}{\cancel{7}}$

$\implies \sf\bold{\purple{100.57\: cm}}$

Now, again long hand it complete 1 revolution in 1 hours :

So, in 48 hours it will take 48 revolution then,

Given :

• Radius = 6 cm

$\implies \sf 2 \times \dfrac{22}{7} \times 6 \times 48$

$\implies \sf \dfrac{44}{7} \times 288$

$\implies \sf \dfrac{\cancel{12672}}{\cancel{7}}$

$\implies \sf\bold{\green{1810.28\: cm}}$

Now, we have to find the sum of distance travelled by their tips in 2 days :

$\implies \sf Total\: distance\: travelled =\: 100.57 + 1810.28$

$\implies \sf\bold{\red{Total\: distance\: travelled =\: 1910.85\: cm}}$

$\therefore$ The sum of distance travelled by their tips in 2 days is 1910.85 cm .