Diameter and length of a roller are 84cm and 120cm .In how many revolutions can the roller level the playground of area 1584m²?
the rolling area of the cylinder is
84*120π cm^2 = 3.17 m^2
now just divide.
To solve this problem, we need to find the number of revolutions needed for the roller to level the playground of area 1584m².
First, we need to find the area covered by one revolution of the roller. The area covered by a roller in one revolution can be calculated using the formula:
Area covered by one revolution = Circumference of the roller × Length of the roller
The circumference of a roller can be calculated using the formula:
Circumference = π × Diameter
Given that the diameter of the roller is 84cm, we can calculate the circumference:
Circumference = π × 84 cm = 264 cm
Now, we need to convert the circumference from centimeters to meters, as the area of the playground is given in square meters. Since there are 100 centimeters in a meter, we divide the circumference by 100 to convert it to meters:
Circumference = 264 cm ÷ 100 = 2.64 m
Next, we can calculate the area covered by one revolution of the roller:
Area covered by one revolution = Circumference × Length
Given that the length of the roller is 120cm, we need to convert it to meters by dividing it by 100:
Length = 120 cm ÷ 100 = 1.2 m
Now, we can calculate the area covered by one revolution of the roller:
Area covered by one revolution = 2.64 m × 1.2 m = 3.168 m²
Finally, we can find the number of revolutions needed to level the playground:
Number of revolutions = Total area of playground ÷ Area covered by one revolution
Given that the total area of the playground is 1584 m², we can calculate the number of revolutions:
Number of revolutions = 1584 m² ÷ 3.168 m² = 500
Therefore, the roller would need 500 revolutions to level the playground of area 1584 m².