Question

The diameter of the wheel of a car is 77cm.How many revolutions will it make to cover a distance of
72.6m?

Answer 1

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Answer 2

$\large{\boxed{\red{\boxed{\underline{\green{\mathscr{Given :-}}}}}}}$

$• \red{\textsf{ Diameter of the wheel = 77 cm}}$

$\large{\boxed{\red{\boxed{\underline{\green{\mathscr{To \: Find :-}}}}}}}$

$• \red{\textsf{ Number of revolutions it will take}}$$\red{\textsf{ to cover a distance of 72.6m}}$

$\large{\boxed{\red{\boxed{\underline{\green{\mathscr{Solution :-}}}}}}}$

$\pink{\textrm{Hence,}}$

$\boxed{\purple{r = \frac{d}{2}}}$

$\pink{\textrm{Therefore,}}$

$\therefore \rm \blue{r = \frac{77cm}{2}}$

$\implies \rm \blue{r = \cancel{\frac{77cm}{2}} = 38.5cm}$

$\large{\bold{\boxed{\underline{\blue{\mathfrak{r = 38.5 cm}}}}}}$

$\pink{\textrm{Hence,}}$

$\large{\boxed{\purple{\textsf{Circumference of Circle = 2 \pi r }}}}$

$\pink{\textrm{Therefore,}}$

$\therefore \rm \blue{Circumference = 2 \times \frac{22}{7} \times 38.5cm}$

$\implies \underline{\bold{\blue{\mathfrak{241.78cm}}}}$

$\pink{\textrm{Hence,}}$

$\large{\boxed{\purple{\mathsf{1cm = \frac{1}{100}m}}}}$

$\pink{\textrm{Therefore,}}$

$\therefore \rm \blue{241.78cm = \frac{241.78}{100}m}$

$\implies \rm \blue{\cancel{\frac{241.78}{100}m} = 2.41m}$

$\boxed{\underline{\purple{\textsf{Circumference of the Circle = }\mathfrak{2.41m}}}}$

$\pink{\textrm{Now,}}$

$\blue{\textsf{Number of Revolution = \frac{72.6m}{2.41m} }}$

$\implies \rm \blue{\cancel{\frac{72.6m}{2.41}} = 30}$

$\implies \bold{\boxed{\underline{\blue{\mathfrak{30 \: revolutions}}}}}$

$\underline{\bold{\purple{\textrm{Hence, number of revolutions}}}}$$\underline{\bold{\purple{\textrm{made by the wheel is 30.}}}}$