Question

a rope has a density and thickness such that a 3.25-centimeter-long segment of it weighs 61.40 grams. there are 28.3495 grams in an ounce and 2.54 centimeters in an inch. how many ounces would a 19.45 inch length of the same rope weigh?
a. 5.10 oz
b. 11.49 oz
c. 32.92 oz
d. 53.90 oz

Explanation:

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<reasoning>

Convert the target length to centimeters

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} L_{\text{cm}} &= 19.45\text{ in} \times 2.54\text{ cm/in} \\ L_{\text{cm}} &= 49.403\text{ cm} \end{aligned}$$

\]

Calculate the mass of the rope in grams

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} \text{Linear Density} &= \frac{61.40\text{ g}}{3.25\text{ cm}} \\ M_{\text{g}} &= 49.403\text{ cm} \times \frac{61.40\text{ g}}{3.25\text{ cm}} \\ M_{\text{g}} &\approx 933.336\text{ g} \end{aligned}$$

\]

Convert the mass from grams to ounces

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} M_{\text{oz}} &= \frac{933.336\text{ g}}{28.3495\text{ g/oz}} \\ M_{\text{oz}} &\approx 32.9225\text{ oz} \end{aligned}$$

\]

Match the calculated value with the options

The calculated mass is approximately \(32.92\text{ oz}\), which corresponds to option (c).
</reasoning>

<answer>
<mcq-option>a. 5.10 oz</mcq-option>
<mcq-option>b. 11.49 oz</mcq-option>
<mcq-correct>c. 32.92 oz</mcq-correct>
<mcq-option>d. 53.90 oz</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert the target length to centimeters

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} L_{\text{cm}} &= 19.45\text{ in} \times 2.54\text{ cm/in} \\ L_{\text{cm}} &= 49.403\text{ cm} \end{aligned}$$

\]

Calculate the mass of the rope in grams

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} \text{Linear Density} &= \frac{61.40\text{ g}}{3.25\text{ cm}} \\ M_{\text{g}} &= 49.403\text{ cm} \times \frac{61.40\text{ g}}{3.25\text{ cm}} \\ M_{\text{g}} &\approx 933.336\text{ g} \end{aligned}$$

\]

Convert the mass from grams to ounces

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} M_{\text{oz}} &= \frac{933.336\text{ g}}{28.3495\text{ g/oz}} \\ M_{\text{oz}} &\approx 32.9225\text{ oz} \end{aligned}$$

\]

Match the calculated value with the options

The calculated mass is approximately \(32.92\text{ oz}\), which corresponds to option (c).
</reasoning>

<answer>
<mcq-option>a. 5.10 oz</mcq-option>
<mcq-option>b. 11.49 oz</mcq-option>
<mcq-correct>c. 32.92 oz</mcq-correct>
<mcq-option>d. 53.90 oz</mcq-option>
</answer>

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