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A boy is cycling such that the wheels of the cycle are making $140$ revolutions per minute. The diameter of the wheel is $60$ cm. Calculate the speed per hour with which the boy is cycling.

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15.84

km/hr

440

km/hr

7.5

km/hr

60

km/hr

answer is A.

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Detailed Solution

It is given that a boy is cycling such that the wheels of the cycle are making

140

revolutions per minute. The diameter of the wheel is

60

cm.
We need to calculate the speed per hour with which the boy is cycling.
We know that the circumference of a circle with radius

r

units is

2 πr

units.
We also know that

d = 2 r

.
Therefore,
Circumference

= πd

units
In this case, the distance the boy covers is equal to the product of the circumference of the wheel and the number of revolutions.
Therefore,

Distance covered = Circumference \times Number of revolutions

\Rightarrow Distance covered = πd \times 140

\Rightarrow Distance covered = \frac{22}{7} \times 60 \times 140

\Rightarrow Distance covered = 26, 400

cm
We know that

1 km = 1, 00, 000 cm

\Rightarrow 26, 400 cm = 0.264 km

We know that

1 \min = \frac{1}{60} hours

.
We know that,

Speed = \frac{Distance covered}{Time taken}

\Rightarrow Speed = \frac{0.264}{(\frac{1}{60})}

\Rightarrow Speed = 0.264 \times 60

\Rightarrow Speed = 15.84

km/hr
Therefore, the speed per hour with which the boy is cycling is

15.84

km/hr.
Hence, the correct option is 1.

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A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. The diameter of the wheel is 60 cm. Calculate the speed per hour with which the boy is cycling.

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Detailed Solution

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A boy is cycling such that the wheels of the cycle are making $140$ revolutions per minute. The diameter of the wheel is $60$ cm. Calculate the speed per hour with which the boy is cycling.