The weight of water is 62 1/2 lb per cubic foot. What is the weight of 7 1/6 cubic feet of water? How much does 7 1/6 cubic feet of water weigh?
The correct answer and explanation is:
Correct Answer:
To find the weight of 7 1/6 cubic feet of water when the weight of 1 cubic foot is 62 1/2 pounds:
Convert the mixed numbers to improper fractions first:
- 62 1/2 = 1252\frac{125}{2}
- 7 1/6 = 436\frac{43}{6}
Now multiply: 1252×436=125×432×6=537512\frac{125}{2} \times \frac{43}{6} = \frac{125 \times 43}{2 \times 6} = \frac{5375}{12}
Now convert 537512\frac{5375}{12} to a mixed number: 5375÷12=447 remainder 115375 \div 12 = 447 \text{ remainder } 11
So, 537512=4471112\frac{5375}{12} = 447 \frac{11}{12}
Final Answer: 447 11/12 pounds
Explanation (300 words):
To calculate the weight of a volume of water, multiply the volume by the weight of one unit of that volume. In this case, the unit volume is 1 cubic foot, and it weighs 62 1/2 pounds. The total volume is 7 1/6 cubic feet. These two values need to be multiplied to find the total weight.
The first step is converting the mixed numbers into improper fractions so they are easier to multiply. The number 62 1/2 becomes 125 over 2, and 7 1/6 becomes 43 over 6. These fractions are then multiplied together. When multiplying fractions, multiply the numerators together and the denominators together. So 125 times 43 equals 5375, and 2 times 6 equals 12. This gives a product of 5375 divided by 12.
The final step is converting this improper fraction into a mixed number. Dividing 5375 by 12 results in 447 with a remainder of 11. This gives the final answer of 447 and 11/12 pounds.
This result means that 7 1/6 cubic feet of water weighs just under 448 pounds. Water is quite heavy when considered in volume, and even a small increase in volume results in a significant weight. This principle is important in many applications, such as construction, plumbing, and engineering, where understanding the load and mass of fluids is critical.