Question

The diameter of a wheel and a car is $ 98 $ cm. How many revolutions will it make to travel $ 6160 $ metres.

Answer 1

Hint: First of all convert the all the given quantities in the same system of the units. Then find the circumference of the circle by using the formula, $ C = 2\pi r $ . Also, by using the correlation between the circumference, distance and the number of revolutions find the required value.

Complete step-by-step answer:
Diameter of the wheel of a car is $ d = 98cm = 0.98m $
Radius, $ r = \dfrac{d}{2} = \dfrac{{0.98}}{2} = 0.49m $
Now, the circumference of the circle is $ c = 2\pi r $
Place the given values in the above expression –
 $ C = 2 \times \dfrac{{22}}{7} \times 0.49 $
Simplify the above expression –
 $ C = 3.08m $
Now, let us assume the number of revolutions be “N”
Also, given the distance to travel is $ d = 6160m $
According to the equation –
 $ N \times 3.08 = 6160 $
Make the required term as the subject –
 $ N = \dfrac{{6160}}{{3.08}} $
Simplify the above expression –
 $ N = 200 $
Hence, the number of revolutions is $ 200 $
So, the correct answer is “200”.

Note: Always remember that the term circumference and the perimeter mean the same. Normally, the length of the straight sided shapes such as square, rectangle, triangles outlines is termed its perimeter and the length of the circle’s outline or any arc’s such as semi-circle outline is so-called its circumference and $ \pi $ is used in the formula whereas perimeter is sum of all the sides using additions. Alternative method to find the perimeter of the circle $ = \pi D $ , where D is the diameter of the circle. Always check the given units of the parameters and the required units of the solution, all should be in the same format of the system of units.