Ex.12.1 Q4 Areas Related to Circles Solution - NCERT Maths Class 10

Go back to  'Ex.12.1'


The wheels of a car are of diameter \(80\, \rm{cm}\) each. How many complete revolutions does each wheel make in \(10\) minutes when the car is traveling at a speed of \(66\, \rm{km}\) per hour?

Text Solution

What is known?

Diameter of the wheel of the car and the speed of the car.

What is unknown?

Revolutions made by each wheel.


Distance travelled by the wheel in one revolution is nothing but the circumference of the wheel itself.


Diameter of the wheel of the car \(= 80\,\rm{cm}\)

Radius \((r)\) of the wheel of the car \(= 40\,\rm{cm}\)

Distance travelled in \(1\) revolution \(=\) Circumference of wheel

Circumference of wheel

\[\begin{align}&= 2\pi \,{ r}\\& = 2\pi \left( {{\text{40}}} \right)\\&= 80\pi\, \rm{cm}\end{align}\]

Speed of car\(= 66\, \text{km/hour}\)

\[\begin{align}&= \frac{{66 \times {\text{ }}100000}}{{60}}\,{\text{cm/}}\,{\text{min}}\\&= 110000 {\text{ cm/min}}\end{align}\]

Distance travelled by the car in \(10\) minutes

\[\begin{align}&= {\text{ }}110000{\text{ }} \times {\text{ }}10{\text{ }}\\&= {\text{ }}1100000{\text{ cm}}\end{align}\]

Let the number of revolutions of the wheel of the car be \(n\)

\(\rm{n} \times\)Distance travelled in\(1\) revolution \(=\)Distance travelled in \(10\) minutes

\[\begin{align}\\\rm{n} \times 80\pi &= 1100000\\{\text{n}} &= \frac{{1100000 \times 7}}{{80 \times 22}}\\ &= \frac{{35000}}{8}\\&= 4375\end{align}\]

Therefore, each wheel of the car will make \(4375\) revolutions.

Learn math from the experts and clarify doubts instantly

  • Instant doubt clearing (live one on one)
  • Learn from India’s best math teachers
  • Completely personalized curriculum

Frequently Asked Questions

What are Class 10 NCERT Exemplars?
While getting good scores in school tests is a desirable outcome, it is not a reliable indicator of how strong your child’s math foundation really is. Many students who score well in school exams in their earlier years, might struggle with math in higher grades because of a weak foundation. At Cuemath, we evaluate your child’s grasp of math fundamentals, and take corrective actions immediately. Also, your child may have limited exposure in their school, and in most cases, may not feel challenged to learn more. Cuemath's customised learning plan ensures your child is challenged with varied difficulty levels of questions at every stage.
What is the difference between CBSE and NCERT syllabus for Class 10?
How will Class 10 NCERT books help in exam preparation?
How will Class 10 NCERT books help you understand basic math concepts?
Which is the best video solution for the class 10 maths NCERT?