QUESTION

# A bicycle wheel makes 5000 revolutions in moving 11 km, then what is the diameter of the wheel?A. 110 cmB. 60 cmC. 220 cmD. 70 cm

Hint: Considering the wheel as a circle, suppose wheel makes 1 revolution then the distance travelled by the wheel in 1 revolution will be equal to the perimeter of the wheel i.e circumference of circle, using formula we can find circumference of circle i.e wheel, then the total distance covered in 5000 revolutions will be 5000 multiplied by perimeter of the wheel which is required answer.

Let us consider that the radius of the wheel is ‘r’ cm.
So, the perimeter of the wheel may be written as:
Perimeter of the wheel = $2\times \pi \times r$
Now, since the total number of revolutions made by the wheel is 5000, so the total distance travelled by the wheel in these 5000 revolutions will be =$5000\times 2\pi r=10000\pi r.........(1)$
Now, it is also given that the wheel has covered a total distance of 11 km in these 5000 revolutions.
Here, we may convert the given distance from ‘km’ to ‘cm’.
So, we know that 1 km = 100000 cm
Therefore, 11 km = 11 × 100000 cm
= 1100000 cm
So, we have the total distance covered by the wheel = 1100000 cm ………….(2)
Therefore, on comparing equation (1) and equation (2), we get:
10000×π×r cm = 1100000 cm
$\pi r=\dfrac{1100000}{10000}cm$
$r=\dfrac{110}{\pi }cm$
$r=\dfrac{110}{\dfrac{22}{7}}cm$
$r=\dfrac{770}{22}cm$
r = 35 cm
Now, we have found the radius of the wheel, so the diameter of the wheel is 2 times the radius.
So, $d=2\times r$
= 70 cm
Hence, (D) 70 cm is the correct option.

Note: Here we may have chances of mistakes due to unit conversion. Since, the distance covered is given in km and options for diameter are given in cm, so the unit from km to cm should be converted properly here.For these types of problems by applying basic geometry we can approach the solution.So,students should remember basic formulas and definitions of geometry.