SOLUTION: 1. The wheel of a wheelbarrow rotates 60 times when it is pushed a distance of 50 metres. Calculate the radius of the wheel, giving you answer to the nearest millimetre. 2. The

1. The wheel of a wheelbarrow rotates 60 times when it is pushed a distance of 50 metres. Calculate the radius of the wheel, giving you answer to the nearest millimetre. 

60 rotations = 50 metres

1 rotation =  metres

Hence, the circumference of the wheel barrow is  m.

Circumference = Pi x diameter  OR Pi x (2 x radius)

 = Pi x 2 x radius

Radius =  = 0.1326 m or 0.133m (3 signficant figures)

2. The wheel on Pip's bicycle has a diameter of 66 cm. Pip cycles a distance of 1000 cm. How many complete rotations does the wheel make?

Circumference of bicycle wheel = Pi x diameter = 207.345cm

So in 1 rotation, his bike will travel 207.345 cm

207.345 cm = 1 rotation

1 cm =  rotations

1000 cm =  rotations = 4.82 rotations

Hence, he makes 4 complete rotations, he has only made 0.82 of the 5th rotation.

The formula for circumference is either:

C = 2pr or C = pd.  

We use the first if we are dealing with the radius,
and we use the second if we are dealing with the diameter.

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1. The wheel of a wheelbarrow rotates 60 times when it is pushed 
a distance of 50 metres. Calculate the radius of the wheel, giving
you answer to the nearest millimetre.

Let the circumference of the wheel be C. Each time the wheel rotates,
the wheelbarrow moves a distance which is equal to the circumference 
of the wheel.  If it rotates 60 times, the wheelbarrow has moved 60 
times the circumference, or 60C.

So we set 60C equal to 50 metres.

60C = 50 metres

  C = 50/60 metres

  C = 5/6 metre 

  C = 2500/3 millimetres

We want the radius, so we use C = 2pr, and substitute 2pr for C

  2pr = 2500/3 millimetres

2pr = 2500/3

Solve for r by dividing both sides by 2p

  r = (2500/3)/(2p)
  r = (2500/3)[1/(2p)]
  r = 2500/(6p)
  r = 1250/(3p)
  r = 132.6291192 or 133 millimetres to the nearest millimeter.

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2. The wheel on Pip's bicycle has a diameter of 66 cm. Pip cycles 
a distance of 1000 cm. How many complete rotations does the wheel 
make?

Let N = the number of rotations the wheel makes.
Let C = the circumference of the wheel.

For each time the wheel rotates, the wheel moves a distance which 
is equal to the circumference of the wheel.  If it rotates N times, 
the wheelbarrow has moved N times the circumference, or NC.  Since 
we are told that the wheel moved 1000 cm, we know that NC must equal 
1000 cm.  So we have the equation

 NC = 1000 cm.

Since we are given the diameter of the wheel, we use the 
circumference formula

C = pd

We are given that the diameter is 66 cm, so we substitute 66 for d

C = p(66)

C = 66p

So we supstitute 66p for C in

 NC = 1000

 N(66p) = 1000

   66pN = 1000

We solve for N by dividing both sides by 66p

      N = 1000/(66p)

      N = 500/(33p)

      N = 4.822877063 or a little less than 5 rotations.  Since 
you are asked for the number of COMPLETE rotations, the answer is 4 
because it doesn't quite complete a fifth rotation.

Edwin