Final answer:
To calculate the volume of the 'scooped' pyramid, integrate the cross-sectional area function over the range of 0 to 5, and multiply it by the height of the pyramid.
Step-by-step explanation:
A 'scooped' pyramid is a pyramid that has a cross-sectional area that changes as you move closer to the tip. In this case, the cross-sectional area is x*4 at a distance x from the tip. The distance from the tip to the base of the pyramid is given as 5 units.
To calculate the volume of the pyramid, we need to integrate the cross-sectional area as we move from the tip to the base. The formula for the volume of a pyramid is V = (1/3) * A * h, where A is the cross-sectional area and h is the height of the pyramid. In this case, the height is given as 5 units.
Using the given information, we can express the cross-sectional area as A(x) = x*4. We integrate this function over the range from 0 to 5, which represents the distance from the tip to the base of the pyramid. The integral of A(x) is (1/2) * x^2 * 4. Plugging in the limits of integration, we get (1/2) * 5^2 * 4 = 50 units cubed.