To find the volume of a rectangular prism (the moving truck, in this case), we can use the formula:
\[ \text{Volume} = \text{length} \times \text{height} \times \text{width} \]
Given the measurements:
- Length: \( 9 \frac{9}{10} \) ft = \( 9.9 \) ft
- Height: \( 6 \frac{1}{10} \) ft = \( 6.1 \) ft
- Width: \( 6 \frac{9}{10} \) ft = \( 6.9 \) ft
Now we can convert these mixed numbers to improper fractions or decimals for easier multiplication:
- Length: \( 9 + \frac{9}{10} = \frac{90}{10} + \frac{9}{10} = \frac{99}{10} \)
- Height: \( 6 + \frac{1}{10} = \frac{60}{10} + \frac{1}{10} = \frac{61}{10} \)
- Width: \( 6 + \frac{9}{10} = \frac{60}{10} + \frac{9}{10} = \frac{69}{10} \)
Now applying the volume formula:
\[ \text{Volume} = \left(\frac{99}{10}\right) \times \left(\frac{61}{10}\right) \times \left(\frac{69}{10}\right) \]
Calculating this step by step:
-
First multiply the numerators: \[ 99 \times 61 \times 69 \] Let's calculate \( 99 \times 61 \): \[ 99 \times 61 = 6039 \] Now multiply \( 6039 \times 69 \): \[ 6039 \times 69 = 416691 \]
-
Now multiply the denominators: \[ 10 \times 10 \times 10 = 1000 \]
-
Putting it all together: \[ \text{Volume} = \frac{416691}{1000} \]
To convert it back to a mixed number: \[ 416691 \div 1000 = 416.691 \]
Thus, the volume of the moving truck is approximately:
\[ 416 \frac{691}{1000} , \text{ft}^3 \]
Therefore, the correct response is:
416 691/1,000 ft.^3