Question

practice: dimensional analysis
show all work as you complete each problem below. make sure to circle or put a box around your final answer and double check your units!

1. 315 cups to liters
2. 125 lbs to grams
3. 11,900 cm to yards
4. 84 cups to gallons
5. 7 feet to kilometers
6. gabi has plans with her friends to go to a concert on her birthday in 4 days. she is so excited that she wants to know how many seconds she has left to wait. can you help her to determine this?
7. your uncle danny just moved into a new apartment and wants to make his famous spaghetti sauce for his new neighbors. unfortunately, he hasn’t unpacked all of his kitchen utensils. his recipe calls for ½ a cup of oregano, however he can only find a teaspoon to measure out his spices. how many teaspoons of oregano would be the same as ½ a cup?
8. lamar has been running sprints to prepare for his next football game. he has found that he can maintain his maximum speed for 45 yards. he’s thinking of running in a 5 km race in a few months, but doesn’t know if he can maintain his maximum speed for the entire 5 km. can you help him determine how far he can?

Explanation:

Problem 1: 315 cups to liters

Step1: Recall conversion factor (1 cup ≈ 0.236588 L)

$315 \text{ cups} \times \frac{0.236588 \text{ L}}{1 \text{ cup}}$

Step2: Multiply to get liters

$315 \times 0.236588 \approx 74.52522$

Step1: Recall conversion factors (1 lb = 453.592 g)

$125 \text{ lbs} \times \frac{453.592 \text{ g}}{1 \text{ lb}}$

Step2: Multiply to get grams

$125 \times 453.592 = 56699$

Step1: Recall conversion factors (1 yard = 91.44 cm)

$11900 \text{ cm} \times \frac{1 \text{ yard}}{91.44 \text{ cm}}$

Step2: Divide to get yards

$\frac{11900}{91.44} \approx 130.14$

Answer:

$\boxed{74.53}$ liters (rounded to two decimal places)

Problem 2: 125 lbs to grams