Question

The wheels of an Audi car has a
diameter of 33 inches. If Ramesh
drives the car at a speed of
180 kms/hr, then find the number
of revolutions made by the wheel
in 11 minutes.​

Answer 1

Given:

The wheels of an Audi car has a diameter of 33 inches. If Ramesh drives the car at a speed of 180 km/hr, then find the number of revolutions made by the wheel in 11 minutes.​

To find:

The number of revolutions made by the wheel in 11 minutes.​

Solution:

Finding the distance covered in 1 revolution:

The diameter of the wheel, d = 33 inches

So, the radius of the wheel,

r = $\frac{d}{2} = \frac{33}{2} = 16.5\: inches = 0.4191 \:m\: . . . \:[since \: 1 \:inch = 0.0254\:m]$

We know,

Distance covered by the wheel in 1 revolution is,

= Circumference of the wheel

= $2\pi r$

= $2 \pi \times 0.4191$

= $0.8382\pi\: meters$

Finding the distance covered in 11 minutes:

Time = 11 minutes = $660 \:seconds \: . . . . \:[since\: 1\: minute = 60 \:seconds]$

The speed of the car = 180 km/hr = $180 \times \frac{5}{18} \:m/s = 50 \:m/s$

We know,

$\boxed{\bold{Speed \times Time = Distance }}$

∴ The distance covered in 11 min or 660 s = $50\:m/s\: \times \:660\:s = 33000\:m$

Finding the no. of revolutions:

The no. of revolutions is,

= $\frac{Total \:distance}{Circumference \:of\:the \:wheel}$

= $\frac{33000}{0.8382\times \frac{22}{7} }$

= $\frac{33000\times 7}{0.8382\times 22 }$

= $12526.84$

≈ $\boxed{\bold{12527}}$

Thus, the number of revolutions made by the wheel in 11 minutes is → 12527.

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Answer 2

Given :  The wheels of an Audi car has a diameter of 33 inches.  

Ramesh drives the car at a speed of 180 kms/hr,

To find : the number of revolutions made by the wheel in 11 minutes.​

Solution:

diameter of 33 inches.  

Circumference = π ( diameter)  = (22/7)  * 33

 one revolution  =  726/7 inches

inch = 2.54 cm

=>   one revolution  = 726 *2.54/ 7  = 1,844.04/7  cm

Ramesh drives the car at a speed of 180 kms/hr,

Distance covered in 1 hr (60 mins) = 180 km

=> Distance covered in 1  mins = 180/60 = 3 km

Distance covered in 11  mins = 11 * 3 = 33 km

33 km = 33000 m = 3300000 cm

=> Number of revolutions = 3300000  / (1,844.04/7)

= 12,526.8

the number of revolutions made by the wheel in 11 minutes.​  =  12526

approx 12527

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