Question

The diameter of a bicycle wheel is 100 cm. How many complete rotations does it make a distance of 2 km?

Answer 1

Answer:

20

Step-by-step explanation:

If a bicycle wheel makes one complete revolution or turn, then the bicycle travels a distance D equal to the wheel's circumference. The circumference C of a circle is the distance around the circle (wheel) and is equal to the number pi (3.14 to two decimal places) times the diameter d of the circle (wheel): C = (pi)d, where, in this case, d = 50 cm.

If a bicycle wheel makes two complete revolutions or turns, then the bicycle travels a distance D equal to twice the wheel's circumference. If a bicycle wheel makes three complete revolutions or turns, then the bicycle travels a distance D equal to three times the wheel's circumference. If a bicycle wheel makes four complete revolutions or turns, then the bicycle travels a distance D equal to four times the wheel's circumference, and so on; therefore, if a bicycle wheel makes "t" complete revolutions or turns, then the bicycle travels a distance D equal to t times the wheel's circumference; therefore, ...

We can write the following formula for finding the distance D traveled by a bicycle when one of its wheels makes "t" complete revolutions or turns:

D = tC, or, since multiplication is commutative,

D = Ct

Now, finding the distance D traveled by a bicycle when one of its wheels of diameter 50 cm. makes 30 turns:

D = Ct

D = [(pi)d]t

Substituting, we get:

D= [(3.14)(50 cm)](30)

= (157)(30) cm

= 4,710 cm is the approximate distance that a bicycle travels when one of its

wheels of diameter 50 cm. makes 20 turns.

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