Question
A full waterbed mattress is 8 ft by 5 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 StartFraction lb Over ft cubed EndFraction
. Find the weight of the water in the mattress to the nearest pound.
Question content area bottom
Part 1
The waterbed mattress contains approximately
enter your response here lb of water.
(Round to the nearest pound.)
. Find the weight of the water in the mattress to the nearest pound.
Question content area bottom
Part 1
The waterbed mattress contains approximately
enter your response here lb of water.
(Round to the nearest pound.)
Answers
GPT-4o mini
To find the weight of the water in the waterbed mattress, we first need to calculate the volume of the mattress and then convert that volume into weight using the density of water.
1. **Calculate the volume of the waterbed mattress**:
The volume \( V \) of a rectangular prism (which is the shape of the mattress) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Given dimensions:
- Length = 8 ft
- Width = 5 ft
- Height = 1 ft
Plugging in the values:
\[
V = 8 \text{ ft} \times 5 \text{ ft} \times 1 \text{ ft} = 40 \text{ ft}^3
\]
2. **Convert the volume to weight**:
The weight of the water can be calculated by multiplying the volume by the weight density of water:
\[
\text{Weight} = V \times \text{density}
\]
Given the density of water is 62.4 lb/ft³:
\[
\text{Weight} = 40 \text{ ft}^3 \times 62.4 \text{ lb/ft}^3
\]
Calculating this:
\[
\text{Weight} = 40 \times 62.4 = 2496 \text{ lb}
\]
Therefore, the weight of the water in the mattress to the nearest pound is:
\[
\text{Weight} \approx 2496 \text{ lb}
\]
Thus, the answer is:
**2496 lb**
1. **Calculate the volume of the waterbed mattress**:
The volume \( V \) of a rectangular prism (which is the shape of the mattress) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Given dimensions:
- Length = 8 ft
- Width = 5 ft
- Height = 1 ft
Plugging in the values:
\[
V = 8 \text{ ft} \times 5 \text{ ft} \times 1 \text{ ft} = 40 \text{ ft}^3
\]
2. **Convert the volume to weight**:
The weight of the water can be calculated by multiplying the volume by the weight density of water:
\[
\text{Weight} = V \times \text{density}
\]
Given the density of water is 62.4 lb/ft³:
\[
\text{Weight} = 40 \text{ ft}^3 \times 62.4 \text{ lb/ft}^3
\]
Calculating this:
\[
\text{Weight} = 40 \times 62.4 = 2496 \text{ lb}
\]
Therefore, the weight of the water in the mattress to the nearest pound is:
\[
\text{Weight} \approx 2496 \text{ lb}
\]
Thus, the answer is:
**2496 lb**