Can't figure this one out....?

Question

A steel reinforcing rod is 12 ft. long and 1" thick in diameter. If a cubic foot of steel weighs 490 lb., how much does the rod weigh (to the nearest pound)?

Can someone explain how to do this?

Answer 1

Who is this mr. runnynose guy to think you can just multiply 12*490?

a steel rod is a long cylinder: ( convert 12 ft to 144 inches for the height of your cylinder, so that you have unit agreement)

V=h*pi*r^2 = 144 * pi * (1/2)^2 = 113.04 in^3( 1 ft/12 in)^3 = .0654166 ft^3 is the volume of your steel rod

now (490 lb / 1ft^3)(.0654166 ft^3) = 32.05 lb

Answer 2

Take the rod to be a cylinder.

The formula for the volume of a cylinder is the area of the circular base (π r²) times the length of the cylinder.
V = π r² L

However, you need everything in the same units (feet) so that you'll end up with cubic feet.

Your *diameter* is 1 inch (1/12 of a foot) which makes your *radius* equal to 1/24 of a foot.

Using the formula, the volume will be:
V = π (1/24)² * 12

That works out to:
V = π / 48
V ≈ 0.0654498469 cu. ft.

And for that volume, you have to multiply by 490 lbs / cu. ft to get the weight.

Weight = (π / 48) * 490
Weight ≈ 10.2083333 π
Weight ≈ 32.070425

Rounded to the nearest pound, the steel reinforcing rod will weigh 32 lbs.

Answer 3

The Rod is basically a cylinder. Use the formula for the volume (in cubic feet) and then multiply the cubic feet by the weight.

Formula: pi * radius2 * height

3.1416 * (1/2 * 1/2) * 144 inches

3.1416 * 1/4 * 144 = 113.0976 Cubic inches

113.0976 / 1728 (to convert to cubic feet) = .06545 Cubic Feet

.06545 * 490 = 32.0705 Lbs.

Answer 4

you find the volume of the rod and the volume of one cubic foot, divide them, times by 100 to get a percentage. then find that percent of the actual weight of the cubic foot of steel.

Answer 5

12 * 490