Question

The diameter of the wheel of a car is 56 cm. How many revolutions will it make to travel 7.7 km?​

Answer 1

Your answer⬆️

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Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The diameter of the wheel of a car is 56 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Number of revolutions the wheel need to make to travel 7.7 km

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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$\boxed { \bold { Radius = \dfrac { Diameter } { 2 } }}$

• $\bold { Radius = \dfrac { 56} { 2 } = 28 \: cm}$

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$\boxed { \bold { 1 \: km = 100000 \: cm } }$

• $\bold { 7.7 \: km = 770000 \: cm }$

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To find the length, the wheel can cover in one revolution we need to calculate the perimeter of the circular wheel

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We know that ,

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$\underline{ \underline{\bold{\texttt{Perimeter of circle :}}}}$

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➠ 2πr ⚊⚊⚊⚊ ⓵

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Where ,

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• r = Radius

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$\underline{ \underline{\bold{\texttt{Perimeter of wheel :}}}}$

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• r = 28

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⟮ Putting the value in ⓵ ⟯

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: ➜ 2πr

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: ➜ $\sf 2 \times \dfrac { 22 } { 7 } \times 28$

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: ➜ 2 × 4 × 22

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: : ➨ 176 cm

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• Hence the perimeter of circular wheel is 176 cm

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$\underline{ \underline{\bold{\texttt{Number of revolutions :}}}}$

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➠ $\sf N = \dfrac { D } { P }$ ⚊⚊⚊⚊ ⓶

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Where ,

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• N = Number of revolutions

• D = Distance

• P = Distance covered in 1 revolution

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$\underline{ \underline{\bold{\texttt{For the given wheel :}}}}$

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• N = N

• D = 176 cm

• P = 770000 cm

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⟮ Putting the values in ⓶ ⟯

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: ➜ $\sf N = \dfrac { D } { P }$

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: ➜ $\sf N = \dfrac { 770000} { 176}$

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: : ➨ N = 4375

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• Hence the wheel will make 4375 revolutions to travel 7.7 km