or

Question

The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible volumes?

18 ft
19 ft
16 ft

Minimum possible volume =
ft³

Maximum possible volume =
ft³

Answer 1

To find the minimum and maximum possible volumes of the rectangular prism, we will consider the potential measurement errors for each dimension.

Assuming each dimension has a maximum measurement error of ±0.5 ft (a common assumption), the dimensions will vary within the following ranges:

1. Length = 18 ft

   • Minimum Length = 18 ft - 0.5 ft = 17.5 ft
   • Maximum Length = 18 ft + 0.5 ft = 18.5 ft

2. Width = 19 ft

   • Minimum Width = 19 ft - 0.5 ft = 18.5 ft
   • Maximum Width = 19 ft + 0.5 ft = 19.5 ft

3. Height = 16 ft

   • Minimum Height = 16 ft - 0.5 ft = 15.5 ft
   • Maximum Height = 16 ft + 0.5 ft = 16.5 ft

Now, we calculate the volumes:

Minimum Possible Volume:

Using the minimum dimensions: \[ \text{Minimum Volume} = \text{Minimum Length} \times \text{Minimum Width} \times \text{Minimum Height} \] \[ \text{Minimum Volume} = 17.5 , \text{ft} \times 18.5 , \text{ft} \times 15.5 , \text{ft} \] Calculating: \[ = 17.5 \times 18.5 = 324.75 \] \[ 324.75 \times 15.5 \approx 5023.625 , \text{ft}^3 \]

Maximum Possible Volume:

Using the maximum dimensions: \[ \text{Maximum Volume} = \text{Maximum Length} \times \text{Maximum Width} \times \text{Maximum Height} \] \[ \text{Maximum Volume} = 18.5 , \text{ft} \times 19.5 , \text{ft} \times 16.5 , \text{ft} \] Calculating: \[ = 18.5 \times 19.5 = 360.75 \] \[ 360.75 \times 16.5 \approx 5962.875 , \text{ft}^3 \]

Final Results:

Thus, the minimum and maximum possible volumes are:

• Minimum possible volume ≈ 5023.625 ft³
• Maximum possible volume ≈ 5962.875 ft³

You can round these values as needed. For significant figures based on the given dimensions, it might be appropriate to round:

• Minimum possible volume = 5024 ft³
• Maximum possible volume = 5963 ft³