Question

The radius of the driving wheel of an engine is 1.75m. How many revolutions will it make in travelling 22 km? (clue: total distance covered - distance covered for 1 revolution = no of revolutions) *distance covered for 1 revolution means circumference of the wheel​

Answer 1

Given:

• The radius of the driving wheel of an engine is 1.75m

To Find:

• How many revolutions will it make in traveling 22 km.

Solution:

First, we have to find the Circumference of the Wheel:

As, we know:

`\bigstar \:{\boxed{ \rm{Circumference_((Circle)) = 2 \pi r }}} \: \bigstar`

where,

• pi (π) = 22/7
• Radius (r) = 1.75m

So, the Circumference of wheel will be:

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) = 2 * (22)/(7) * 1.75 }}}}`

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) = (2 * 22)/(7) * 1.75}}}}`

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) = (44)/(7) * 1.75 }}}}`

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) = (44 * 1.75)/(7) }}}}`

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) = (77)/(7) }}}}`

`{\large{\rm{\dashrightarrow{Circumference_((Wheel)) ={ \boxed{ \rm{ \red{11m}}}}}}}}`

Hence, the circumference of the wheel is 11m.

Now, we have to convert distance covered km into m:

`{\leadsto{\large{\rm{ \: Distance \: Covered = 22km}}}}`

`{\leadsto{\large{\rm{ \: Distance \: Covered =(22 * 1000)m }}}}`

`{\leadsto{\large{\rm{ \: Distance \: Covered = {\boxed{\rm{\red{22000m}}}}}}}}`

Hence, the distance covered is 22000m.

Now, we have to find the number of revolution:

Given:

• Circumference = 11m
• Distance Covered = 22000m

According to the question by using the formula, we get:

`\bigstar \: { \boxed{ \large{ \rm{Number \: of \: Revolution \: = \: (Distance \: Covered)/(Circumference )}}}}`

`{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = (22000)/(11) }}}}`

`{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = { \boxed{\red{2000}}}}}}}`

Thus, the revolution will it make in traveling 22km is 2000.