Question

the wheels of a car are of diameter 80 cm each how many complete revolutions does each wheel make in 10 min when the car is traveling at a speed of 66 km per hour​

Answer 1

Given :-

• Diameter of circle = 80 cm

• Speed = 66 km/hr

• Time taken = 10 mins

To Find :-

• Number of revolutions.

Solution :-

We know that,

$\red\bigstar\:\:\:\boxed{\underline{{\sf Number\: of \:revolutions =\dfrac{ Total \:Distance}{Distance \:covered \:in \:1 \:revolution} }}}$

Radius of the circle :-

⇒  Diameter/2

⇒  80/2

⇒  40 cm.

Distance covered in 1 revolution :-

⇒  Circumference of circle

⇒  2πr

⇒  2 × π × 40

⇒  80π cm.

As per the question :-

• Speed = 66 km/hr

• Time = 10 min = 10/60 hr = 1/6 hr

Distance covered by the wheel :-

$\pink{:\implies\:\:}\sf{Speed = \dfrac{Distance}{Time} }$

$\pink{:\implies\:\:}\sf{66 = \dfrac{Distance}{\frac{1}{6} } }$

$\pink{:\implies\:\:}\sf{Distance=66\times \dfrac{1}{6} }$

$\pink{:\implies\:\:}\sf{Distance=11 \:km }$

∴  Distance covered = 11 km.

Total distance covered :-

⇒  11 × 1000 m

⇒  11000 m

⇒  11000 m × 100 cm

⇒  1100000 cm

Number of revolutions :-

$\green{:\implies\:\:}\sf{\dfrac{1100000}{80 \pi } }$

$\green{:\implies\:\:}\sf{\dfrac{110000}{8 \pi } }$

$\green{:\implies\:\:}\sf{\dfrac{110000}{8 \times \frac{22}{7} } }$

$\green{:\implies\:\:}\sf{\dfrac{110000\times 7}{8 \times 22 } }$

$\green{:\implies\:\:}\sf{\dfrac{770000}{176 } }$

$\green{:\implies\:\:}\sf{4375 }$

∴ Number of revolutions is 4375.