Question

How many times does a wheel of radius 42m rotate to cover a distance of 396 m

Answer 1

Answer :-

• The wheel will rotate 1.5 times to cover a distance of 396 m.

Given :-

• The radius of a wheel is 42 m.

To find :-

• The number of times the wheel will rotate to cover a distance of 396 m.

Step-by-step explanation :-

• The distance covered by the wheel in one rotation will be equal to it's circumference.

• So, to find the number of times the wheel will rotate to cover a distance of 396 m, we first have to find the circumference of the wheel.

• Here, the radius of the wheel has been given to us, we will use it to find its circumference.

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We know that :-

$\underline{\boxed{\sf Circumference \: of \: a \: circle= 2 \pi r}}$

Where,

• r = Radius.
• π = pi.

Here,

• Radius = 42 m.
• pi = 22/7.

$\underline{\underline{\mathfrak{Substituting \: the\: given\: values,}}}$

$\boxed{\tt Circumference = 2 \times \dfrac{22}{\cancel{7}} \times \cancel{42}}$

Reducing the numbers,

$\boxed{\tt Circumference = 2 \times \dfrac{22}{1} \times 6}$

Multiplying 22/1 with 6,

$\boxed{\tt Circumference = 2 \times \dfrac{132}{1}}$

Now let's multiply the remaining numbers, since we can't reduce them anymore.

$\boxed{\tt Circumference = 2 \times 132}$

Multiplying the numbers,

$\overline{\boxed{\tt Circumference = 264 \: m}}$

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• The circumference of the wheel is 264 m, which means that the wheel covers a distance of 264 m on rotating once.

• So now let's find the number of times the wheel will rotate to cover a distance of 396 m.

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The number of times the wheel should rotate is equal to :-

$\underline{\boxed{\sf \dfrac{Distance\: to \: be \:covered}{Distance\: covered\: in \: one \:rotation}}}$

Here,

• Distance to be covered = 396 m.
• Distance covered in 1 rotation = 264 m.

Hence,

The number of times the wheel will rotate is :-

$\overline{\boxed{\tt \dfrac{396}{264} = 1.5}}$

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• So, the wheel will rotate 1.5 times to cover a distance of 396 m.

Answer 2

Answer :

$\large \implies \sf 1\frac{1}{2} Rotation .$

Solution :

Given :

• Radius of wheel = 42m.
• Distance covered = 396m.

To Find :

• Number of rotation to cover a distance of 396m.

$\large \red \bigstar \boxed{\tt Circumference \: of \: circle = \: 2\pi r }$

• Circumference of wheel = 2πr

$\: \: \: \: \: \: \sf \implies 2 \times \frac{22}{7} \times 42 \\ \\ \: \: \: \: \: \: \sf \implies\boxed{ \sf 264m}$

• Number of Rotation to cover 396m =

$\: \: \: \: \: \: \sf = \frac{Total \: Distance\: Covered}{ Distance\: Covered\: in \: one \: rotation} \\ \\ \large \: \: \: \: \: \: \sf \implies \frac{396}{264} \\ \\ \large \: \: \: \: \: \: \sf \implies 1\frac{1}{2} Rotation \\ \\ \large \: \: \: \: \: \: \sf \implies \boxed{\mathfrak{1.5 rotation} }$

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