Final answer:
To find the volume of the wedge in the figure, integrate the area of vertical cross sections using the given dimensions. The volume is 4 units cubed.
Step-by-step explanation:
To find the volume of the wedge in the figure, we will integrate the area of vertical cross sections. Let's define the dimensions given in the question:
- Length (L) = 9
- Width (W) = 2
- Height (H) = 6
To integrate the area of vertical cross sections, we need to choose a variable to represent the width of each cross section. Let's use 'x' for this variable. Since the wedge has a constant width of 2, the area of each cross section is 2x. We can integrate this area over the length of the wedge (from x = 0 to x = 2) to find the total volume.
Therefore, the volume of the wedge is given by the integral of 2x with respect to x, evaluated from 0 to 2:
V = ∫(0 to 2) 2x dx
Using the power rule of integration, we can find the antiderivative of 2x, which is x^2. Evaluating this antiderivative from 0 to 2:
V = (2^2) - (0^2)
V = 4 - 0 = 4
So, the volume of the wedge is 4 units cubed.