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Mensuration
<div>A lawnmower takes 750 complete revolutions to cut grass on a field. Calculate the area of the field if the diameter of the lawnmower is 84 cm and the length is 1 m.</div>
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1 Reply
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To calculate the area of the field covered by the lawnmower, we need to consider the path traced by the lawnmower as it takes 750 complete revolutions.
First, let’s calculate the circumference of the lawnmower’s cutting area:
Circumference = π * diameter Circumference = 3.14 * 84 cm Circumference = 263.76 cm
Now, we need to convert the length of the lawnmower from meters to centimeters:
Length = 1 m = 100 cm
The area covered by each revolution of the lawnmower is the product of the circumference and the length:
Area covered by each revolution = Circumference * Length Area covered by each revolution = 263.76 cm * 100 cm Area covered by each revolution = 26376 cm^2
To find the total area of the field, we multiply the area covered by each revolution by the number of revolutions:
Total area = Area covered by each revolution * Number of revolutions Total area = 26376 cm^2 * 750 Total area = 19,782,000 cm^2
Therefore, the area of the field covered by the lawnmower is 19,782,000 square centimeters (cm^2).
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