A steel post is 6 ft. long and 6" thick in diameter. If a cubic foot of steel weighs 490 lb., how much does the rod weigh (to the nearest pound)?

Correct answer is 577 pounds.

To find the weight of the steel rod, we need to calculate its volume.

1. Let's start by converting the dimensions of the rod to feet, as the weight of steel is given in pounds per cubic foot.
Length: 6 ft.
Diameter: 6" = 6/12 = 0.5 ft.

2. The volume of a cylinder can be calculated using the formula:
V = πr²h
where V is the volume, π is a constant (approximately 3.14159), r is the radius of the base, and h is the height.

3. Since the given diameter is 0.5 ft, the radius (r) would be half of that:
r = 0.5/2 = 0.25 ft.

4. We can calculate the volume of the rod:
V = π(0.25)²(6) ≈ 0.2955 ft³. (approximated to 4 decimal places)

5. Now, to find the weight of the rod, we can multiply the volume by the weight per cubic foot of steel:
Weight = Volume × Weight per cubic foot of steel
Weight = 0.2955 ft³ × 490 lb/ft³

6. Calculating the weight:
Weight ≈ 144.3985 lb. (approximated to 4 decimal places)

Therefore, the weight of the steel rod is approximately 144 pounds.

To find the weight of the steel rod, we need to calculate its volume first. The volume of a cylinder (which the steel rod resembles) can be found using the formula:

V = π * r^2 * h

Where:
V is the volume
π is a mathematical constant approximately equal to 3.14159
r is the radius of the cylinder (half of the diameter)
h is the height (or length) of the cylinder

Given that the diameter of the steel rod is 6 inches, the radius would be half of that, which is 3 inches (or 0.25 feet). And the height (length) is given as 6 feet. Let's calculate the volume:

V = 3.14159 * (0.25)^2 * 6

V ≈ 0.589 ft^3

Now, we can find the weight of the rod by multiplying its volume by the weight of steel per cubic foot:

Weight = V * Weight of steel per cubic foot

Weight = 0.589 ft^3 * 490 lb/ft^3

Weight ≈ 288 lb

Therefore, the weight of the steel rod is approximately 288 pounds.

V = 3.14 * 0.75 * 6

V = 14.13 cubic feet

14.13 * 490 = 6,924 lbs.