Question

the radius of a wheel is 14 cm. find the number of times the wheel revolves to cover a distance of 110 m​

Answer 1

★ Concept

In order to solve this question you must be aware of two things. Firstly, Distance covered by a wheel in 1 revolution is equals to the Circumference (Perimeter) of a wheel. Secondly (one of the basic), that a wheel is in a shape of circle so, we will apply a formula for Circumference of Circle i.e, 2πr. Afterthat, we will use the concept of 'Unitary Method'. [Must pay attention to the units].

Let's proceed with Calculation !!

$\rule{190pt}{1pt}$

Formula used

$\underline{ \boxed{ \green{\sf \: Circumference \: of \: Circle = 2\pi r}}}$

$\underline{\boxed{ \red{\sf \: Distance \: covered \: by \: a \: wheel \: (in \: 1 \: rev) = Circumference \: of \: a \: wheel }}}$

Given, Radius of a wheel = 14 cm.

Circumference of a wheel = 2πr

(Taking, π = 22/7)

>> Circumference of wheel = 2*22/7*14

Circumference of wheel = 44*2 = 88 cm

[Distance covered by a wheel in 1 revolution = Circumference (or Perimeter) of wheel].

Distance covered in 1 revolution = 88 cm

>> To Calculate :-

The number of times the wheel revolves to cover a distance of 110 m (or 11,000 cm).

✦ By Unitary Method

>> A Distance of 88 cm = 1 Revolution.

>> Distance of 1 cm = 1/88 Revolution.

Distance of 11000 cm = 11000/88 Revol. = 125 Revolution

Distance of 110 m = 125 revolutions.

$\underline{ \rule{190pt}{2pt}}$

Note ::

Distance covered by a wheel in 110 m = Distance covered by a wheel in 11000 cm. Since, 1 m = 100 cm ; 110 m = 11000 cm

[You may also convert 'cm' into 'm', the answer would remain unaltered i.e 125 times revolution].

Answer 2

$\huge\underline{\underline{\mathfrak\red{Given::}}}$

$\small\text{The radius of a wheel is 14 cm.} \\ \small\text{find the number of times the wheel } \\ \small\text{revolves to cover a distance of 110 m }$

$\huge\underline{\underline{\mathfrak\red{Solution::}}}$

$\small\text{The distance a wheel travels in one rotation =} \\ \small\text\red{{The circumference of the circle.}}$

$\bf{ Radius(r)=\red{14 \: cm}} \\ \\ \bf{Circumference =\red{2\pi \: r}} \\ \\ \bf{\implies\red{2 \times \frac{22}{7} \times 14}} \\ \\ \bf{\implies\red{ \frac{22}{7} \times 28}} \\ \\ \bf{\implies\red{ \frac{22}{\cancel7} \times \cancel { 28} } } \\ \\ \bf{\implies\red{ 88 \: cm}}$

$\text{Wheel can travel \red{88 cm} in 1 rotation} \\ \text{It has to cover\red{ 110 metres (11000 cm)}} \\ \\ \bf{So \: \frac{11000}{88} = \red{ 125}} \\ \\ \text{So wheel rotates \red{125 times} to travel 22 meters.}\\ \\ \boxed{\mathfrak\green{Hope \: it\: helps}}$