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A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.
Given:
A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions.
To do:
We have to find the radius of its wheels.
Solution:
Distance covered in 1 revolution $=$ Circumference of the wheel of the car
Distance covered by the car in 450 revolutions $= 1\ \mathrm{~km}= 1000\ \mathrm{~m}$
This implies,
Distance covered in 1 revolution $=\frac{1000}{450}\ \mathrm{~m}$
$=\frac{20}{9}\ \mathrm{~m}$
The circumference of the wheel of the car $=\frac{20}{9} \mathrm{~m}$
Let $r$ be the radius of the wheel.
This implies,
$2 \pi r=\frac{20}{9}\ \mathrm{~m}$
$\Rightarrow \frac{2 \times 22}{7} r=\frac{20}{9}\ \mathrm{~m}$
$\Rightarrow r=\frac{20 \times 7}{9 \times 2 \times 22}\ \mathrm{~m}$
$\Rightarrow r=\frac{35}{99} \mathrm{~m}$
$\Rightarrow r=\frac{35 \times 100}{99} \mathrm{~m}$
$\Rightarrow r=\frac{3500}{99} \mathrm{~m}$
$\Rightarrow r=35.35 \mathrm{~m}$
The radius of the wheels of the car is $35.35 \mathrm{~m}$.
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