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Mathematics

A wheel has diameter 84 cm. Find how many complete revolutions must it make to cover 3.168 km.

Mensuration

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Answer

Diameter of the wheel = 84 cm

Radius of the wheel = d2\dfrac{d}{2} = 842\dfrac{84}{2} = 42 cm

Circumference of the wheel = 2πr

=2×227×42=2×22×6=264 cm= 2 \times \dfrac{22}{7} \times 42\\[1em] = 2 \times 22 \times 6\\[1em] = 264 \text{ cm}

Let the wheel make n revolutions.

Total distance traveled by the wheel = n x Circumference of the wheel

⇒ 3.168 km = n x 264 cm

⇒ 316,800 cm = n x 264 cm

⇒ n = 316,800264\dfrac{316,800}{264}

⇒ n = 1200

Hence, the wheel makes 1,200 revolutions.

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