A company makes steel rods shaped like cylinders. Each rod has a diameter of
8
centimeters and a height of
30
centimeters. The company uses, on average,
94,953.6cm^3
of steel each hour to make these rods. How many rods does the company make, on average, each hour?
For your calculations, do not round any intermediate steps, and use the
π
button on the ALEKS calculator. Round your answer to the nearest hundredth.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius (half the diameter) and h is the height.
In this case, the diameter is 8 cm, so the radius is 8/2 = 4 cm. The height is 30 cm.
The volume of each rod is V = π(4^2)(30) = 480π cm^3.
The company uses 94,953.6 cm^3 of steel each hour.
To find out how many rods the company makes in an hour, we divide the total volume used by the volume of each rod.
Number of rods = (94,953.6 cm^3) / (480π cm^3) ≈ 63.08 rods.
Rounding to the nearest hundredth, the company makes about 63.08 rods each hour.
To find the volume of each steel rod, we can use the formula for the volume of a cylinder: V = π * r^2 * h, where V is the volume, r is the radius (half the diameter), and h is the height.
Given:
Diameter = 8 cm
Radius (r) = Diameter/2 = 8/2 = 4 cm
Height (h) = 30 cm
Let's substitute the values in the formula to find the volume of each rod.
V = π * (4 cm)^2 * 30 cm
V = π * 16 cm^2 * 30 cm
V = 480π cm^3
The company uses 94,953.6 cm^3 of steel in 1 hour.
To find how many rods the company makes in 1 hour, we divide the total volume of steel used by the volume of each rod.
Number of rods = Total volume of steel used / Volume of each rod
Number of rods = 94,953.6 cm^3 / 480π cm^3
Now let's calculate this using the π button on the calculator.
Number of rods = 199.88 rods
Therefore, on average, the company makes approximately 199.88 rods per hour (rounded to the nearest hundredth).