Question

a rod of iron of uniform density has a thickness such that a one-inch-long segment of it weighs 3.88 ounces. given that there are 0.035273 ounces in a gram and 2.54 centimeters in an inch, how many grams would a 14.79 cm length of the same iron rod weigh?
a. 73.30 g
b. 274.49 g
c. 640.51 g
d. 1,626.89 g

Explanation:

Convert the rod length from centimeters to inches

Using the Unit Conversion and Dimensional Analysis knowledge points

$$ L_{\text{in}} = \frac{14.79\text{ cm}}{2.54\text{ cm/in}} \approx 5.82283\text{ inches} $$

Calculate the weight of the rod in ounces

Using the Linear Density knowledge point

$$ W_{\text{oz}} = 5.82283\text{ inches} \times 3.88\text{ ounces/inch} \approx 22.5926\text{ ounces} $$

Convert the weight from ounces to grams

Using the Unit Conversion and Dimensional Analysis knowledge points

$$ W_{\text{g}} = \frac{22.5926\text{ ounces}}{0.035273\text{ ounces/gram}} \approx 640.51\text{ grams} $$

Answer:

• a. 73.30 g
• b. 274.49 g
• c. 640.51 g (Correct answer)
• d. 1,626.89 g