Question

The diameter of a cycle's wheel is 2.1 m. If the cycle covers 7.128 km distance in one hour, then the number of revolutions of the wheel in one minute is​

Answer 1

Answer:

18 Revolutions

Step-by-step explanation:

Given,

Radius = Diameter/2 = 2.1/2 = 1.05 m

Distance covered in 1 hour = 7.128 km = 7128 m

To find,

No. of revolutions in one minute = ?

Solution :

Circumference = 2πr

⇒ 2×22/7×1.05

⇒6.6 metres

Now no. of revolutions in a hour = 7128/6.6 m

⇒ 1080 revolutions in one hour

Now,

No. of revolutions in a minute = 1080/60

⇒18 revolutions in a minute

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Answer 2

Given:

The diameter = 2× radius = 2.1 m.

Cycle covers 7.128 km distance in one hour,

Solution:

Understand that the distance covered in one revolution is equal to the perimeter of the cycle's wheel,

Therefore the distance covered in one revolution is,

$\[\begin{array}{l} = 2\pi r\\ = \pi \times \left( {2r} \right)\\ = \frac{{22}}{7} \times 2.1\\ = 6.6{\rm{ m}}\end{array}\]$

Know that the distance covered in one hour is 7.128 km.

Therefore the distance in meter, covered in one minute

$\[\begin{array}{l} = \frac{{7.128 \times 1000}}{{60}}\\ = 1188\end{array}\]$

Now, the number of revolutions of the wheel in one minute is​,

$\[{\rm{ = }}\frac{{{\rm{Distance travels in one minute}}}}{{{\rm{Distance coverd in one revolution}}}}\]$

$\[\begin{array}{l}{\rm{ = }}\frac{{1188}}{{6.6}}\\ = 18\end{array}\]$

Hence, the number of revolutions of the wheel in one minute is 18.