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Work out the circumference of a circle with a diameter of 8 cm - Junior Cycle Mathematics - Question 10 - 2019
Question 10
Work out the circumference of a circle with a diameter of 8 cm. Give your answer correct to one decimal place. The rubber track for a toy digger goes around four ci... show full transcript
Worked Solution & Example Answer:Work out the circumference of a circle with a diameter of 8 cm - Junior Cycle Mathematics - Question 10 - 2019
Step 1
Work out the circumference of a circle with a diameter of 8 cm.
Answer
To find the circumference of a circle, we can use the formula:
C = ext{diameter} imes rac{ ext{pi}}{1}
Substituting the diameter:
C = 8 imes rac{22}{7} ext{ (using an approximate value for } ext{pi})
Calculating this gives:
Correcting this to one decimal place, the circumference is:
25.1 cm.
Step 2
Calculate the length of the rubber track that goes around the four wheels.
Answer
The rubber track goes around four wheels, thus the total length can be calculated as:
where C represents the distance between the wheels. Here, we have:
Diameter of each wheel = 8 cm Thus,
So, we substitute into the formula:
Therefore, the total length is:
73.0 cm.
Step 3
Work out how many times each wheel will turn fully when the digger travels a distance equal to the length of its rubber track.
Answer
Since one complete turn of the wheel covers a distance equal to its circumference, we can determine the number of turns by using:
ext{Number of Turns} = rac{ ext{Total Distance}}{ ext{Circumference of One Wheel}}
From part (a), we found: 25.1 cm as the circumference of one wheel. Thus:
Now substituting:
ext{Number of Turns} = rac{73.1}{25.1} = 2.9
Rounding down, the number of complete turns is:
2 full turns.