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Answer :
To determine how much the steel reinforcing rod weighs, we need to calculate its volume and then use the density of steel to find its weight.
Here's a step-by-step explanation:
1. Understand the shape of the rod: The rod is cylindrical, so we will use the formula for the volume of a cylinder. The formula is:
[tex]\[
V = \pi \times r^2 \times h
\][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius of the cylinder, and [tex]\( h \)[/tex] is the height (or length) of the cylinder.
2. Convert dimensions:
- The diameter of the rod is given as 1 inch. The radius is half of the diameter, so the radius is 0.5 inches.
- We need to work in feet for consistency with the given weight of steel, so convert the radius from inches to feet:
[tex]\[
\text{Radius in feet} = \frac{0.5 \text{ inch}}{12} = \frac{1}{24} \text{ feet}
\][/tex]
3. Calculate the volume of the rod:
- With the radius [tex]\(\frac{1}{24}\)[/tex] feet and the length of the rod 12 feet, plug these into the cylinder volume formula:
[tex]\[
V = \pi \times \left(\frac{1}{24}\right)^2 \times 12
\][/tex]
4. Calculate the weight:
- We know that 1 cubic foot of steel weighs 490 pounds. So, we multiply the volume of the rod by this density to find the weight:
[tex]\[
\text{Weight} = \text{Volume} \times 490
\][/tex]
5. Result:
- The weight of the rod, rounded to the nearest pound, is approximately [tex]\(32\)[/tex] pounds.
So, the steel reinforcing rod weighs 32 pounds.
Here's a step-by-step explanation:
1. Understand the shape of the rod: The rod is cylindrical, so we will use the formula for the volume of a cylinder. The formula is:
[tex]\[
V = \pi \times r^2 \times h
\][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius of the cylinder, and [tex]\( h \)[/tex] is the height (or length) of the cylinder.
2. Convert dimensions:
- The diameter of the rod is given as 1 inch. The radius is half of the diameter, so the radius is 0.5 inches.
- We need to work in feet for consistency with the given weight of steel, so convert the radius from inches to feet:
[tex]\[
\text{Radius in feet} = \frac{0.5 \text{ inch}}{12} = \frac{1}{24} \text{ feet}
\][/tex]
3. Calculate the volume of the rod:
- With the radius [tex]\(\frac{1}{24}\)[/tex] feet and the length of the rod 12 feet, plug these into the cylinder volume formula:
[tex]\[
V = \pi \times \left(\frac{1}{24}\right)^2 \times 12
\][/tex]
4. Calculate the weight:
- We know that 1 cubic foot of steel weighs 490 pounds. So, we multiply the volume of the rod by this density to find the weight:
[tex]\[
\text{Weight} = \text{Volume} \times 490
\][/tex]
5. Result:
- The weight of the rod, rounded to the nearest pound, is approximately [tex]\(32\)[/tex] pounds.
So, the steel reinforcing rod weighs 32 pounds.
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