The diameter of a roller is 80 cm and its length is 126 cm. It takes 750 complete revolution once over to level a playground. find the area of the ground.
the roller's curved surface area is
2pi r h = 2pi * 40 * 126 = 31667 cm^2
750 revolutions will thus cover 23750420 cm^2 = 2375 m^2
Well, let's start by finding the circumference of the roller. The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 80 cm, so the circumference is 80π cm.
Now, let's find the distance covered by the roller in one complete revolution. Since the circumference represents the distance covered in one revolution, it means that the roller covers 80π cm in one revolution.
Since it takes 750 complete revolutions to level the playground, the total distance covered by the roller would be 750 times the circumference, which is 750 * 80π cm.
The area of the ground can be calculated by multiplying the total distance covered by the roller by the length of the roller. In this case, the length is 126 cm. So, the area of the ground is 750 * 80π * 126 cm².
Now, I'm not sure about you, but I'm not a fan of doing all that math. So, I'll leave the calculator duty to you. Just remember to include the π in your calculations. Good luck!
To find the area of the ground, we need to calculate the total distance covered by the roller as it makes 750 complete revolutions.
First, let's find the circumference of the roller using the diameter provided:
Circumference = π * diameter
Circumference = 3.14 * 80 cm
Circumference = 251.2 cm
The roller covers this distance for each revolution.
Next, let's find the total distance covered by the roller in 750 revolutions:
Total distance = circumference * number of revolutions
Total distance = 251.2 cm * 750
Total distance = 188,400 cm
Since the roller covers this distance to level the ground, the area of the ground is equal to the product of the total distance covered and the length of the ground (assuming the roller covers a strip of ground with the same width as its length):
Area of the ground = Total distance * length
Area of the ground = 188,400 cm * 126 cm
Area of the ground = 23,718,400 cm^2
Therefore, the area of the ground is 23,718,400 cm^2.
To find the area of the ground, we need to use the formula for the surface area of a cylinder. The formula is given by:
Surface area = 2πr² + 2πrh
Where:
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the cylinder
- h is the height of the cylinder
In this case, the roller can be considered as a cylinder. The length of the roller represents the height (h) of the cylinder. To calculate the area of the ground, we need to find the radius (r) of the roller.
The diameter of the roller is given as 80 cm. The radius (r) can be found by dividing the diameter by 2:
r = diameter / 2 = 80 cm / 2 = 40 cm
Now, let's calculate the surface area of the roller:
Surface area = 2πr² + 2πrh
= 2 × 3.14 × (40 cm)² + 2 × 3.14 × (40 cm) × (126 cm)
Simplifying the equation:
Surface area = 2 × 3.14 × 1600 cm² + 2 × 3.14 × 5040 cm²
= 10048 cm² + 31689.6 cm²
= 41737.6 cm²
Therefore, the area of the ground is approximately 41737.6 cm².