Respuesta :
Answer:
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:
[tex] \bigstar \:{\boxed{ \rm{Circumference_{(Circle)} = 2 \pi r }}} \: \bigstar[/tex]
where,
- pi (π) = 22/7
- Radius (r) = 1.75m
So, the Circumference of wheel will be:
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = 2 \times \frac{22}{7} \times 1.75 }}}} [/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{2 \times 22}{7} \times 1.75}}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44}{7} \times 1.75 }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44 \times 1.75}{7} }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{77}{7} }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} ={ \boxed{ \rm{ \red{11m}}}}}}}}[/tex]
Hence, the circumference of the wheel is 11m.
Now, we have to convert distance covered km into m:
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered = 22km}}}}[/tex]
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered =(22 \times 1000)m }}}}[/tex]
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered = {\boxed{\rm{\red{22000m}}}}}}}}[/tex]
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:
[tex] \bigstar \: { \boxed{ \large{ \rm{Number \: of \: Revolution \: = \: \frac{Distance \: Covered}{Circumference }}}}}[/tex]
[tex]{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = \frac{22000}{11} }}}}[/tex]
[tex]{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = { \boxed{\red{2000}}}}}}}[/tex]
