Question

The wheel of a cart is making 20 revolutions per second. If the diameter of the
wheel is 112 cm, find its speed in km/h,

Answer 1

GIVEN:-

• $\rm{ No.\:of\: revolution\:per\:second = 20}$

• $\rm{Diameter\:of\:the\:wheel = 112cm}$

TO FIND:-

• Find its Speed in km/h.

FORMULAE USED:-

• ${\boxed{\rm{Circumference = 2 \pi r}}}$

• ${\boxed{\rm{Speed = \dfrac{Distance}{Time}}}}$.

HOW TO SOLVE:-

• Firstly, we will find the distance by finding the Circumference of the wheel.

• We then will multiply it by the number of revolution done by wheel we will get the total distance covered.

Now,

$\implies\rm{ Radius = \dfrac{Diameter}{2}}$

$\implies\rm{ Radius = \dfrac{112}{2}}$

$\implies\rm{ Radius = 56cm}$

Therefore,

$\implies\rm{ Circumference = 2\pi r}$

$\implies\rm{ Circumference = 2\times{\dfrac{22}{7}}\times{56}}$

$\implies\rm{ Circumference = 11 \times{8} = 88cm}$

• Circumference = Distance

$\implies\tt{ Distance\: covered \:in\:20\: Revolution = 88\times{20}}$

$\implies\tt{ Distance\: covered \:in\:20\: Revolution = 1760cm}$

Henceforth,

$\implies\rm{ Distance = 1360cm = 0.0136km}$

$\implies\rm{ Time = 1 second = \dfrac{1}{3600}hr}$

$\implies\rm{ Speed = \dfrac{Distance}{Time}}$

$\implies\rm{ Speed = \dfrac{0.0136}{\dfrac{1}{3600}}}$

$\implies\rm{ Speed = 0.0136\times{3600}}$

$\implies\rm{ Speed = 48.96km/hr}$

Hence, The Speed of wheel is 48.96km/h

Answer 2

Given :

• No. of revolution per second = 20
• Diameter of the wheel = 112cm

Find :

• Speed of the wheel (km/hr)

Solution :

=> Radius = Diameter/2

=> Radius = 112/2

=> Radius = 56cm

=> Circumference = 2πr

=> Circumference = 2 * 22/7 * 56

=> Circumference = 11 * 8

=> Circumference = 88

=> Distance covered in 20 revolution = 88×20

=> Distance covered in 20 revolution = 1760cm

=> Distance = 1360cm (0.0136 km)

=> Time = 1second = 1/3600hr

=> Speed = Distance/Time

=> Speed = 0.0136 × 3600

=> Speed = 48.96 km/hr

Therefore, Speed of wheel is 48.96 km/hr

hope it helps ! ( ◜‿◝ )♡