Question

The tyre of a truck completes 2100 revolutions to cover a distance of 8.8 km. What is the diameter of the tyre?
A. 1m
B. $\dfrac{3}{2}$m
C. $\dfrac{4}{3}$m
D. $\dfrac{5}{4}$m

Answer 1

Hint:The circumference is the perimeter of a circle or ellipse in geometry. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the arc length of the circle. The perimeter, in general, is the length of any closed figure's curve. Hence to find the revolutions the following formula is used.

Formula used:
Circumference of a circle = $2\pi r$
2r = d
R – radius of the circle
d – diameter of the circle

Complete step-by-step solution:
The circumference of a circle is the distance around it, however if distance is defined in terms of straight lines, as it is in many introductory presentations, this cannot be used as a definition. As the number of sides rises without restriction, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons. When measuring physical things and contemplating abstract geometric shapes, the term circumference is used. One of the most significant mathematical constants is connected to the circumference of a circle. The Greek letter is used to symbolise the constant$\pi $pi.
So now for the solution
Number of revolutions x Circumference = Distance covered.
2100 × $\pi $d = 8800
Now we find d using $\pi = \dfrac{{22}}{7}$
$d = \dfrac{{8800 \times 7}}{{2100 \times 22}}$
$ \Rightarrow d = \dfrac{4}{3}$
Hence option C is correct.

Note:Keep in mind that 2 r = d and not 2d = r
Also the value of $\pi $ is to be memorized.
The girth of an undirected graph is defined as the length of the graph's shortest cycle in graph theory. If the graph does not include any cycles (i.e., if it is a forest), its girth is infinite. A 4-cycle (square), for example, has girth 4. Girth 4 is also found in a grid, and girth 3 is found in a triangular mesh. Triangle-free graphs have girths of four or greater.