To find the volume of Nicol's watermelon slice, which approximates the shape of a rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to determine the base area. The base is a rectangle, and its area can be calculated using the formula for the area of a rectangle:
\[ \text{Base Area} = \text{width} \times \text{length} \]
Given:
- Width = 1.1 inches
- Length = 105 inches
- Height = 8 inches
Let's calculate the base area:
\[ \text{Base Area} = 1.1 , \text{inches} \times 105 , \text{inches} = 115.5 , \text{inches}^2 \]
Now, we can use the base area to find the volume:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting the values we have:
\[ V = \frac{1}{3} \times 115.5 , \text{inches}^2 \times 8 , \text{inches} \]
Calculating it step-by-step:
- Calculate the product of base area and height:
\[ 115.5 , \text{inches}^2 \times 8 , \text{inches} = 924 , \text{inches}^3 \]
- Now calculate the volume:
\[ V = \frac{1}{3} \times 924 , \text{inches}^3 = 308 , \text{inches}^3 \]
So, the approximate volume of Nicol's watermelon slice is:
\[ \boxed{308 , \text{inches}^3} \]