Question

Hey!!

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?​

Answer 1

Given :

• Diameter of a wheel of a car = 80 cm
• The speed of the car = 66 km/hr
• Time in which the car covers a particular distance at a speed of 66 km/hr = 10 minutes

To find :

• Number of complete revolutions the car makes in 10 minutes

Concept Used :

Formula to calculate distance :-

$\boxed{ \sf{ \pmb{ \blue{Distance = Speed \times Time}}}} \quad \star$

Formula to calculate radius :-

$\boxed{ \sf{ \pmb{ \blue{Radius = \dfrac{Diameter}{2} }}}} \quad \star$

Formula to calculate circumference of circle :-

$\boxed{ \sf{ \pmb{ \blue{Circumference = 2\pi r}}}} \quad \star$

where,

• Take π = 22/7
• r = radius

Solution :

Firstly, we will calculate the distance travelled by the car in 10 minutes.

For that we will convert the time from 10 minutes into hrs first.

As we know,

• 1 min = 1/60 hr

Divide the value by 60 to convert it from minutes into hr.

→ Time = 10 min = 10/60 hr

Using formula,

$\\ \dashrightarrow \quad \sf Distance = Speed \times Time$

Substituting the given values,

$\\ \dashrightarrow \quad \sf Distance = 66 \times \dfrac{10}{60}$

$\\ \dashrightarrow \quad \sf Distance = 66 \times \dfrac{1 \not0}{ 6 \not0}$

$\\ \dashrightarrow \quad \sf Distance = \not66 \times \dfrac{1}{ \not6}$

$\\ \dashrightarrow \quad \sf Distance = 11$

$\\ \dashrightarrow \quad \sf \red{Distance = 11 \: km}$

Now,

Convert the distance covered by the car in 10 minutes from km into cm.

For that, multiply the value by 100000 cm.

→ Distance = 11 km = 11 × 100000 = 1100000 cm.

Now, Calculate the circumference of the wheel. For that firstly, find the radius.

Using formula,

$\\ \dashrightarrow \quad\sf Radius = \dfrac{Diameter}{2}$

Substituting the given values,

$\\ \dashrightarrow \quad\sf Radius = \dfrac{80}{2}$

$\\ \dashrightarrow \quad\sf Radius = \dfrac{ \not80}{ \not2}$

$\\ \dashrightarrow \quad\sf Radius = 40$

$\\ \dashrightarrow \quad\sf \red{Radius \: \: of \: \: the \: \: wheel = 40 \: cm}$

Using formula,

$\\ \dashrightarrow \quad \sf Circumference = 2\pi r$

Substituting the given values,

$\\ \dashrightarrow \quad \sf Circumference = 2 \times \dfrac{22}{7} \times 40$

$\\ \dashrightarrow \quad \sf Circumference = \dfrac{1760}{7} cm \: or \: 251.43 \: cm$

Number of revolutions × Circumference = Distance travelled in 10 minutes

$\\ \dashrightarrow \quad \sf No. \: \: of \: \: revolutions \times \dfrac{1760}{7} = 11$

$\\ \dashrightarrow \quad \sf No. \: \: of \: \: revolutions = 1100000 \times \dfrac{7}{1760}$

$\\ \dashrightarrow \quad \sf No. \: \: of \: \: revolutions = 110000 \not0 \times \dfrac{7}{176 \not0}$

$\\ \dashrightarrow \quad \sf No. \: \: of \: \: revolutions = 110000 \times \dfrac{7}{176}$

$\\ \dashrightarrow \quad \sf No. \: \: of \: \: revolutions = 4375$

$\\ \star \quad \sf \blue{No. \: \: of \: \: revolutions \: \: that \: \: the \: \: car \: \: makes \: \: in \: 10 \: minutes \: = 4375}$