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Answer :
To find out how much the cast iron bar weighs, follow these steps:
1. Convert the Dimensions to Inches:
- The dimensions given are [tex]\(5.5\)[/tex] feet by [tex]\(6\)[/tex] inches by [tex]\(2\)[/tex] inches.
- Since [tex]\(1\)[/tex] foot equals [tex]\(12\)[/tex] inches, convert the length from feet to inches:
[tex]\[
5.5 \text{ feet} = 5.5 \times 12 = 66 \text{ inches}
\][/tex]
2. Calculate the Volume of the Cast Iron Bar:
- Use the formula for volume to find the volume in cubic inches, which is:
[tex]\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\][/tex]
- Substitute the dimensions into the formula:
[tex]\[
\text{Volume} = 66 \text{ inches} \times 6 \text{ inches} \times 2 \text{ inches} = 792 \text{ cubic inches}
\][/tex]
3. Determine the Weight:
- You know that cast iron weighs approximately [tex]\(0.25\)[/tex] pounds per cubic inch.
- Calculate the weight by multiplying the volume by the weight per cubic inch:
[tex]\[
\text{Weight} = 792 \text{ cubic inches} \times 0.25 \text{ lbs/cubic inch} = 198 \text{ pounds}
\][/tex]
Therefore, the weight of the cast iron bar is 198 pounds, which corresponds to option (a).
1. Convert the Dimensions to Inches:
- The dimensions given are [tex]\(5.5\)[/tex] feet by [tex]\(6\)[/tex] inches by [tex]\(2\)[/tex] inches.
- Since [tex]\(1\)[/tex] foot equals [tex]\(12\)[/tex] inches, convert the length from feet to inches:
[tex]\[
5.5 \text{ feet} = 5.5 \times 12 = 66 \text{ inches}
\][/tex]
2. Calculate the Volume of the Cast Iron Bar:
- Use the formula for volume to find the volume in cubic inches, which is:
[tex]\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\][/tex]
- Substitute the dimensions into the formula:
[tex]\[
\text{Volume} = 66 \text{ inches} \times 6 \text{ inches} \times 2 \text{ inches} = 792 \text{ cubic inches}
\][/tex]
3. Determine the Weight:
- You know that cast iron weighs approximately [tex]\(0.25\)[/tex] pounds per cubic inch.
- Calculate the weight by multiplying the volume by the weight per cubic inch:
[tex]\[
\text{Weight} = 792 \text{ cubic inches} \times 0.25 \text{ lbs/cubic inch} = 198 \text{ pounds}
\][/tex]
Therefore, the weight of the cast iron bar is 198 pounds, which corresponds to option (a).
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