Answer :
Final answer:
To determine the number of cups of cocoa powder needed, convert 12 ounces to grams, calculate the volume in cubic centimeters, and then convert to cups. The recipe requires approximately 2.178 cups of cocoa powder.
Explanation:
To find out how many cups of cocoa powder are needed, we need to convert 12 ounces to grams then find the volume in cubic centimeters before converting to cups.
First, convert ounces to grams using the conversion factor 28.4 g = 1 oz.:
- 12 oz × 28.4 g/oz = 340.8 g
Next, using the fact that 1 cm3 of cocoa powder weighs 0.652 grams, we find the volume:
- Volume in cm3 = 340.8 g ÷ 0.652 g/cm3
- Volume in cm3 = 522.788 cm3
Now, convert cm3 to tablespoons, knowing that 1 Tbsp = 15 mL = 15 cm3:
- 522.788 cm3 ÷ 15 cm3/Tbsp = 34.853 Tbsp
Finally, as 1 cup equals 16 tablespoons, divide the total tablespoons by 16:
- 34.853 Tbsp ÷ 16 Tbsp/cup = 2.178 cups
Therefore, you will need approximately 2.178 cups of cocoa powder for your recipe.
Final answer:
To convert 12 ounces of cocoa powder into cups, first convert the weight to grams (340.8g), then to volume in mL (522.71 mL), and finally to cups, resulting in approximately 2.18 cups needed for the recipe.
Explanation:
The question requires converting ounces to cups for cocoa powder using the given density and volume conversions. First, we need to convert the required 12 ounces of cocoa powder to grams. Using the conversion factor 1 ounce is equivalent to 28.4 grams, we calculate:
12 oz × 28.4 g/oz = 340.8 g
Given the density of cocoa powder as 0.652 grams per cm3, we can find the volume in cubic centimeters (cc3) or milliliters (mL), since 1 mL = 1 cc3:
340.8 g ÷ 0.652 g/cm3 = 522.71 cm3 or mL
Knowing that 1 cup is equal to 240 mL (since 1 cup = 16 tablespoons and 1 tablespoon = 15 mL), we can now convert the volume to cups:
522.71 mL ÷ 240 mL/cup = approximately 2.18 cups
Therefore, you will need roughly 2.18 cups of cocoa powder for the recipe.
