Final answer:
The density of water in pounds per cubic foot is 62.4 lb/ft³. This is determined by converting the known density of water from grams per cubic centimeter to pounds per cubic foot using conversion factors, including the conversion from grams to pounds and cubic centimeters to cubic feet.
Step-by-step explanation:
The density of water is a commonly known physical property and is a fundamental concept taught in physics. To answer the question: What is the density of water in pounds per cubic foot? The correct option is (a) 62.4 lb/ft³. Here's how you can understand this conversion:
The density of water at 4°C (39.2°F) is about 1 g/cm³. To convert this to pounds per cubic foot, we use conversion factors. Knowing that there are 454 grams in a pound and there are 12 inches in a foot, which gives us 1728 cubic inches in a cubic foot (since 12³ = 1728), we can perform the conversion.
To convert grams to pounds, we use the ratio 454 g = 1 lb. To convert cubic centimeters to cubic feet, we understand that each side of a cubic foot is 12 inches long, and each inch is 2.54 centimeters, therefore one cubic foot is 12 x 2.54 cm³, cubed, which is 1728 x (2.54³) cm³. Finally, we can calculate the density in pounds per cubic foot by multiplying the density in grams per cubic centimeter by the conversion factors needed to move from grams to pounds, and from cubic centimeters to cubic feet.
The calculated value is approximately 62.4 pounds per cubic foot, which is often cited as the density of water in engineering and scientific calculations.