Question

the diameter of a wheel is 105cm.what will be the number of rotations of the wheel to cover a distance of 330m.​

Answer 1

Answer:

Given:-

• Diameter of a wheel = 105cm

• Total distance covered = 330m

To Find:-

• Number of rotations of the wheel to cover a distance of 330m.

Formula used:-

• Circumference of circle = 2πr

Solution:-

As given,

Diameter = 105m then,

Radius = $\dfrac{105}{2}$m

And,

We can write 330m as 33000cm.

Now,

Circumference of the wheel = 2πr

= $2 × \dfrac{22}{7}×\dfrac{105}{2}$

= $22 × 15$

= $330cm$

Now,

No. of rotation

= $\dfrac{Distance\: covered}{Circumference \:of \:wheel}$

= $\dfrac{33000}{330}$

= $100$

Hence, the number of rotation of the wheel to cover 330m (33000cm) are 100.

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Answer 2

ANSWER :

• ❖ If the diameter of a wheel is 105 cm; then the number of rotations of the wheel to cover a distance of 330 m is 100.

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SOLUTION :

❒ Given :-

• Diameter of the wheel = 105 cm

❒ To Calculate :-

• Number of rotations of the wheel to cover a distance of 330 m = ?

❒ Required formulas :-

• Circumference of a circle = 2 × π × Radius

• Radius = $\sf{\dfrac{Diameter}{2}}$

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❒ Calculation of the radius of the wheel :-

Given that,

• Diameter = 105 cm

We know that,

• $\dag \: \: \underline{ \boxed{ \sf{ \: Radius =\dfrac{Diameter}{2}} \: \: }}$

Using this formula,

• ✪ Radius of the wheel = $\sf{\dfrac{105 \: cm}{2}}$

➜ Radius of the wheel = 52.5 cm

• Hence, radius of the wheel is 52.5 cm.

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❒ Calculation of the circumference of the wheel :-

Here,

• Radius = 52.5 cm

• π = $\sf{\dfrac{22}{7}}$

We know that,

• $\dag \: \underline{ \boxed{ \sf{ \: Circumference \: \: of \: \: a \: \: circle = 2 \times \pi \times Radius \: }}}$

Using this formula,

• ✪ Circumference of the wheel = (2 × $\sf{\dfrac{22}{7}}$ × 52.5 ) cm

➜ Circumference of the wheel = ( $\sf{\dfrac{2310}{7}}$ ) cm

➜ Circumference of the wheel = 330 cm

∴ Circumference of the wheel = 3.3 m

• Hence, circumference of the wheel is 3.3 m.

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❒ Calculation of number of rotation :-

We have,

• Distance covered by the wheel = 330 m

• Circumference of the wheel = 3.3 m

Suppose,

• Number of rotation = n

According to question,

• ★ n × Circumference of the wheel = Distance covered by the wheel

⇒ n × 3.3 m = 330 m

⇒ n = $\sf{\dfrac{330 \: m}{3.3 \: m}}$

∴ n = 100

• Thus, the required number of rotation is 100.