For small paving jobs, a contractor uses a roller pushed by a worker.
A roller pushed by a worker (radius=8 in; length=30 in.)
To the nearest square inch, what is the area of pavement with which the surface of the roller will come into contact in one complete rotation?
A 753 in.²
B 1,507 in.²
C 1,708 in.²
D 1,909 in.²
length = circumference of roller = 2π(8) = 16π
width = 30
area = 30(16π) = 480π in^2
=2(pi)rh
=2(pi)(8)(30)
=1507 in^2
So the answer is B
To calculate the area of pavement that the surface of the roller will come into contact with in one complete rotation, we need to find the surface area of the roller.
Step 1: Calculate the lateral surface area of the roller.
Lateral surface area = circumference × length
The circumference of the roller can be calculated using the formula:
Circumference = 2 × π × radius
The radius of the roller is given as 8 inches.
Circumference = 2 × 3.14 × 8 = 50.24 inches
Now, calculate the lateral surface area:
Lateral surface area = 50.24 inches × 30 inches = 1507.2 square inches
Therefore, to the nearest square inch, the area of pavement that the surface of the roller will come into contact with in one complete rotation is 1,507 square inches.
The answer is B) 1,507 in.²
To find the area of pavement with which the surface of the roller will come into contact in one complete rotation, we need to calculate the surface area of the roller.
The roller is a cylinder, and the formula to calculate the surface area of a cylinder is:
Surface Area = 2πr(r + h)
where r is the radius of the base and h is the height (or length) of the cylinder.
In this case, the radius (r) is given as 8 inches and the length (h) is given as 30 inches.
Substituting the values into the formula, we get:
Surface Area = 2π(8)(8 + 30)
= 2π(8)(38)
= 2π(304)
= 608π
Now, to approximate the area to the nearest square inch, we need to calculate the value of π (pi) and then multiply it by 608.
π (pi) is a mathematical constant, approximately equal to 3.14159.
Multiplying 3.14159 by 608, we get:
Approximate Area = 3.14159 * 608
≈ 1909
Hence, the approximate area of pavement with which the surface of the roller will come into contact in one complete rotation is 1,909 in.².
Therefore, the answer is option D: 1,909 in.².