To find the volume of a rectangular prism, you can use the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
First, let's convert the mixed numbers into improper fractions or decimals for easier computation:
- Height: \( 10 \frac{1}{2} = \frac{21}{2} \) inches
- Length: \( 6 \frac{2}{3} = \frac{20}{3} \) inches
- Width: \( 2 \frac{1}{4} = \frac{9}{4} \) inches
Now, substituting the values into the volume formula:
\[ \text{Volume} = \left(\frac{20}{3}\right) \times \left(\frac{9}{4}\right) \times \left(\frac{21}{2}\right) \]
Let's calculate this step by step:
- Calculate \( \frac{20}{3} \times \frac{9}{4} \):
\[ \frac{20 \times 9}{3 \times 4} = \frac{180}{12} = 15 \]
- Now multiply by \( \frac{21}{2} \):
\[ 15 \times \frac{21}{2} = \frac{315}{2} = 157.5 \]
So, the volume of the rectangular prism is:
\[ 157.5 \text{ in}^3 \]
Now, let's check if this volume can hold an item with a height of 8 in., a length of 6 in., and a width of 2 in.:
The volume of the item can also be calculated using the same formula:
\[ \text{Volume of the item} = 6 \times 2 \times 8 = 96 \text{ in}^3 \]
Since \( 157.5 \text{ in}^3 > 96 \text{ in}^3 \), the prism is large enough to hold the item.
Thus, the final answers are:
- Volume of the rectangular prism: \( 157.5 \text{ in}^3 \)
- Yes, it is large enough to hold the item.