Question

Say true and false.
The wheels of a car are of diameter 80cm each. It will make 4300 complete revolutions in 10 minutes. Then the car is travelling at a speed of 66 km per hour.
$
  (a){\text{ True}} \\
  (b){\text{ False}} \\
 $

Answer 1

Hint – In this question, find the circumference of the wheels which is $2\pi r$ as the wheels are circular in shape. The total distance travelled by the car can be calculated via the multiplication of circumference and the total revolutions.
Complete step-by-step answer:
Given data
Diameter of the wheel of the car = 80 cm.
It makes 4300 complete revolutions in 10 minutes.
As we know that the radius (r) of the wheel is half of the diameter.
$ \Rightarrow r = \dfrac{d}{2} = \dfrac{{80}}{2} = 40$cm.
Now the circumference (C) of the wheel is = $2\pi r$cm.
$ \Rightarrow C = 2\pi r = 2 \times \dfrac{{22}}{7} \times 40 = \dfrac{{1760}}{7}$ cm. $\left[ {\because \pi = \dfrac{{22}}{7}} \right]$
Now total distance (S) travelled by the car is the multiplication of circumference and total revolutions.
$ \Rightarrow S = \dfrac{{1760}}{7} \times 4300$ cm.
Now as we know speed (v) is the ratio of distance (S) to time (t),
And it takes 10 minutes to complete 4300 revolutions.
$ \Rightarrow v = \dfrac{S}{t} = \dfrac{{\dfrac{{1760}}{7} \times 4300}}{{10}}$ cm/min.
Now as we know 60 min = 1hour.
Therefore 10 min = (10/60) = (1/6) hour.
And 100 cm = 1m
And 1000 m = 1km.
Therefore 100000cm = 1km.
Therefore $\dfrac{{1760}}{7} \times 4300$ cm = $\dfrac{{\dfrac{{1760}}{7} \times 4300}}{{100000}}$ km
$ \Rightarrow v = \dfrac{{\dfrac{{\dfrac{{1760}}{7} \times 4300}}{{100000}}}}{{\dfrac{1}{6}}} = \dfrac{{\dfrac{{1760}}{7} \times 4300 \times 6}}{{100000}}$ Km/hr.
Now on simplify we have,
$ \Rightarrow v = 64.868$ Km/hr.
So the given statement is false.
Hence option (B) is correct.

Note – The key point here was the conversion of units from cm and minutes into kilometers and hours respectively. It is always advised to remember basic conversion units like 1 hour = 60 minutes, 100 cm = 1m, 1000 m = 1km and thus 100000cm = 1km.