Question

The Wheels of a car are of diameter 80cm each how many complete revolutions does each wheel make in 10 minutes and the car is travelling at the speed of 66 km per hour

Answer 1

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Answer 2

$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,

Diameter of the wheel of a car $d = 80\: cm$

Speed of the car $s = 66\: kmph$

No. of complete revolutions made by each wheel in $\textit{10\: minutes}$= ?

$\underline{\large{\textsf{Step-1:}}}$
Find the radius of wheel of the car.

Since,
Shape of the wheel of a car is $\textsf{Circle}$

We have,
$\bigstar \textsf{ For a Circle, Diameter = 2 \times radius}$

$\implies radius\: (r) = \dfrac{Diameter\: (d)}{2}$

$\implies r = \dfrac{80\: cm}{2} = 40\: cm$

Radius of the Wheel $r = 40\: cm$

$\underline{\large{\textsf{Step-2:}}}$
Find the Circumference of the wheel

$\bigstar \textsf{Circumference of the circle, C = 2 \pi r}$

Substituting values
$\implies C = 2 \times \pi \times 40 = 80\pi$

Circumference of the wheel $C = 80\pi\: cm$

$\underline{\large{\textsf{Step-3:}}}$
Note the Distance covered by car in one revolution of it's wheel

Distance covered by car in one revolution of it's wheel is equal to $\textsf{Circumference of it's wheel}$

$\implies$ Distance covered by car in one revolution of it's wheel = $80\pi\: cm$

$\underline{\large{\textsf{Step-4:}}}$
Express time taken (10 minutes) in Hours

We have,
$\bigstar \textsf{1 Hour = 60 Minutes}$

Divide with 6 on both sides

$\implies 10\: Min = \dfrac{1}{6}\: Hr$

$\underline{\large{\textsf{Step-5:}}}$
Find the total distance covered in 10 minutes

We have,
$\bigstar \textbf{Speed = \dfrac{Distance\: covered}{time\: taken} }$

Substituting Values

$\implies 66\: kmph = \dfrac{Distance\: covered}{\frac{1}{6}\: hr}$

$\implies Distance\: covered = 66\: kmph \times \frac{1}{6}\: hr}$

$\implies Total\: Distance\: covered\: in\: 10\: min= 11\: km$

$\underline{\large{\textsf{Step-6:}}}$
Express Distance covered by car in cm
(As the given data is in cm

We have,
$\bigstar \textsf{1\: km = 1000\: m}$
$\bigstar \textsf{1\: m = 100\: cm}$

$\implies 1\: km = 1000 \times 100\: cm$

$\implies 1\: km = 100000\: cm$

Multiply with 11 on Both Sides

$\implies 11\: km = 1100000\: cm$

Distance covered by car = $1100000\: cm$

$\underline{\large{\textsf{Step-7:}}}$
Find the No. of revolutions made by wheel of the car in 10 minutes

$\bigstar \mathbf{No.\: of\: revolutions\: made\: by\: car\: in\: 10\: min = \dfrac{Total\: distance\: covered\: in\: 10\: min}{Distance\: covered\: in\: 1\: revolution\: of\: it's\: wheel}}$

Substituting Values

$\implies$ No. of revolutions = $\dfrac{1100000}{80\pi}$

$\implies$ No. of revolutions = $\dfrac{110000}{8 \times \frac{22}{7}}$

$\implies$ No. of revolutions = $\dfrac{110000 \times 7}{8 \times 22}$

$\implies$ No. of revolutions = $4375$

$\therefore$

$\bigstar \textsf{In 10 minutes, No. of revolutions made by car's wheel = \underline{\textbf{4375}}}$