Water weighs about 63 pounds per cubic foot. A king size water bed mattress measures 5.5 ft by 6.5 ft by 8 in deep. How much does the water in this mattress weigh?
The correct answer and explanation is:
Step 1: Convert Inches to Feet
The depth of the mattress is given as 8 inches. Since there are 12 inches in a foot, we convert: 8 inches÷12=0.6667 feet8 \text{ inches} \div 12 = 0.6667 \text{ feet}
Step 2: Calculate the Volume of the Mattress
The mattress dimensions in feet are:
- Length = 5.5 ft
- Width = 6.5 ft
- Depth = 0.6667 ft
The volume is calculated using the formula for the volume of a rectangular prism: Volume=Length×Width×Depth\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} =5.5×6.5×0.6667= 5.5 \times 6.5 \times 0.6667 =23.916 cubic feet= 23.916 \text{ cubic feet}
Step 3: Calculate the Weight of the Water
Water weighs 63 pounds per cubic foot, so we multiply: 23.916×63=1,507.7 pounds23.916 \times 63 = 1,507.7 \text{ pounds}
Final Answer:
The water in the king-size mattress weighs approximately 1,508 pounds.
Explanation:
A waterbed is essentially a large bladder filled with water, and its weight depends on the volume of water it holds. The calculation is straightforward by determining the total volume of the mattress in cubic feet and then multiplying it by the known weight of water per cubic foot. This weight is significant and explains why waterbeds require sturdy floor support.
Since the mattress holds over 1,500 pounds of water, it is crucial to consider flooring strength before placing it in a home. Older homes with weak floors may not support this much weight in one concentrated area. Additionally, moving a filled waterbed is impractical, so draining is required before relocation.
Now, let’s generate an image of a king-size waterbed filled with water to visualize the concept.
Here is the generated image of a king-size waterbed filled with water. It visually represents the concept of a large water-filled mattress in a modern bedroom setting. Let me know if you need any modifications!
