Answer

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**Hint**First calculate the distance covered by the motorcycle in given time using the following formula

${\text{Distance covered = Number of revolutions x Circumference of the wheel}}$

Circumference of the wheel = Circumference of the circle =$\pi {R^2}$

Where, R = Radius of the wheel

Next use the relation between speed, time and distance to get the answer.

**Complete step by step solution**

We know distance covered by the wheel is given by

${\text{Distance covered = Number of revolutions x Circumference of the wheel}}$

Circumference of the wheel = Circumference of the circle =$\pi {R^2}$

Where, R = Radius of the wheel

According to the problem

R = \[{\text{70/2}}\] = 35 cm (we divided 70 by 2 because 70 is the diameter of the wheel)

Number of revolutions = 40

Time = 10 second

$\therefore $Distance covered in 40 second = $40\times\pi \times{35^2}$cm

= 8800 cm

= 88 m

Or, Distance covered in 1 second = \[{\text{88/10}}\] = 8.8 m

Now,

$Speed = \dfrac{{Dis\tan ce}}{{Time}}$

Or, $Speed = \dfrac{{8.8}}{1}$ m/sec = \[{\text{8}}{\text{.8 m/sec}}\]

Again, to convert m/sec to km/hr we multiply m/sec with \[{\text{18/5}}{\text{.}}\]

$\therefore $ Speed = $8.8\times\dfrac{{18}}{5}$ km/hr =\[{\text{31}}{\text{.68 km/hr}}{\text{.}}\]

**(Option C)**

**Note:**We are using the formula of circumference of the circle because wheels are in the form of a circle. In 1 revolution the motorcycle covers the distance equal to the circumference of the wheel. In the above question the value of π is 3.14 as the question does not mention its value however in case it is mentioned in the question used that value only. To convert m/sec to km/hr multiply m/sec with 18/5 and to convert km/hr to m/sec multiply km/hr with 5/18. You may remember this by remembering 18>5 is similar to km>m so in case we are going to km/hr from m/sec 18 will be in the numerator and 5 in denominator and vice-versa.

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