Answer
Verified
378k+ views
Hint: We are given that a bus has a wheel with a given diameter and it makes \[20,000\] rotations to travel from one town to the other and we are asked to calculate the distance covered by the train. We know that the wheel is in the shape of 2D circle. And the distance that will be covered in one rotation is equal to the circumference of the circle, which is, \[2\pi r\]. So, for \[20,000\] rotations, we will multiply the circumference by \[20,000\]. On solving, we will have the distance covered by the bus while travelling from one town to another.
Complete step-by-step solution:
According to the given question, we are given a bus which has wheels of diameter \[1.4m\]. The wheels complete \[20,000\] rotations while the bus travels from one town to other and we are asked to find the distance covered by the bus for the same.
The given diameter of the wheel is, \[d=1.4m\]
The radius of the wheel is, \[r=\dfrac{1.4}{2}=0.7m\]
We know that the wheel is in the shape of 2D circle. And the distance that will covered in one rotation is equal to the circumference of the circle, which is, \[2\pi r\].
So, the distance covered in \[20,000\] rotation of the wheel is,
\[= 20000\times 2\pi r\]
We will now substitute the known values and we get,
\[= 20000\times 2\times \dfrac{22}{7}\times 0.7\]
\[= 20000\times 2\times \dfrac{22}{7}\times \dfrac{7}{10}\]
Cancelling out the common terms, we get the expression as,
\[= 20000\times 2\times \dfrac{22}{10}\]
\[= 2000\times 2\times 22\]
\[= 88000m\]
\[= 88km\]
Therefore, the distance covered by the bus is (A) \[88km\].
Note: The formula for the circumference of the circle should be written correctly. Also, while substituting the values in the expression, make sure that the values are orderly put without any mistakes. Do not take the value of the diameter of the wheel directly, first find the radius and then use it in the formula for the circumference of a circle.
Complete step-by-step solution:
According to the given question, we are given a bus which has wheels of diameter \[1.4m\]. The wheels complete \[20,000\] rotations while the bus travels from one town to other and we are asked to find the distance covered by the bus for the same.
The given diameter of the wheel is, \[d=1.4m\]
The radius of the wheel is, \[r=\dfrac{1.4}{2}=0.7m\]
We know that the wheel is in the shape of 2D circle. And the distance that will covered in one rotation is equal to the circumference of the circle, which is, \[2\pi r\].
So, the distance covered in \[20,000\] rotation of the wheel is,
\[= 20000\times 2\pi r\]
We will now substitute the known values and we get,
\[= 20000\times 2\times \dfrac{22}{7}\times 0.7\]
\[= 20000\times 2\times \dfrac{22}{7}\times \dfrac{7}{10}\]
Cancelling out the common terms, we get the expression as,
\[= 20000\times 2\times \dfrac{22}{10}\]
\[= 2000\times 2\times 22\]
\[= 88000m\]
\[= 88km\]
Therefore, the distance covered by the bus is (A) \[88km\].
Note: The formula for the circumference of the circle should be written correctly. Also, while substituting the values in the expression, make sure that the values are orderly put without any mistakes. Do not take the value of the diameter of the wheel directly, first find the radius and then use it in the formula for the circumference of a circle.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE