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Answer :
To determine the weight of a steel reinforcing rod that is 12 feet long and 1 inch in diameter, we can follow these steps:
1. Convert the Diameter to Feet:
- The diameter of the rod is given in inches (1 inch). We need to convert this to feet since the length is in feet.
- There are 12 inches in a foot. So, the diameter in feet is [tex]\( \frac{1}{12} \)[/tex] feet.
2. Calculate the Radius:
- The radius is half of the diameter. Therefore,
[tex]\[
\text{Radius} = \frac{1 \text{ inch in feet}}{2} = \frac{1}{24} \text{ feet}.
\][/tex]
3. Determine the Volume of the Rod:
- The rod is a cylinder, so we use the formula for the volume of a cylinder: [tex]\( V = \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height (or length).
- Substitute the values:
[tex]\[
V = \pi \times \left(\frac{1}{24}\right)^2 \times 12.
\][/tex]
4. Calculate the Weight:
- The weight is found by multiplying the volume by the weight of one cubic foot of steel.
- We have the weight per cubic foot as 490 pounds.
- Calculate the weight:
[tex]\[
\text{Weight} = V \times 490.
\][/tex]
After performing these calculations, we find that the weight of the rod is approximately 32 pounds. Therefore, the rod weighs 32 pounds to the nearest pound.
1. Convert the Diameter to Feet:
- The diameter of the rod is given in inches (1 inch). We need to convert this to feet since the length is in feet.
- There are 12 inches in a foot. So, the diameter in feet is [tex]\( \frac{1}{12} \)[/tex] feet.
2. Calculate the Radius:
- The radius is half of the diameter. Therefore,
[tex]\[
\text{Radius} = \frac{1 \text{ inch in feet}}{2} = \frac{1}{24} \text{ feet}.
\][/tex]
3. Determine the Volume of the Rod:
- The rod is a cylinder, so we use the formula for the volume of a cylinder: [tex]\( V = \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height (or length).
- Substitute the values:
[tex]\[
V = \pi \times \left(\frac{1}{24}\right)^2 \times 12.
\][/tex]
4. Calculate the Weight:
- The weight is found by multiplying the volume by the weight of one cubic foot of steel.
- We have the weight per cubic foot as 490 pounds.
- Calculate the weight:
[tex]\[
\text{Weight} = V \times 490.
\][/tex]
After performing these calculations, we find that the weight of the rod is approximately 32 pounds. Therefore, the rod weighs 32 pounds to the nearest pound.
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