Final answer:
The volume of the pyramid Francine wants to construct, in terms of the base length b, is V = (2/3) × b³ + 67 × b², where the height is given as h = 2b + 201.
Step-by-step explanation:
Francine wants to construct a pyramid where the height (h) is 201 millimeters more than twice the base length (b). To write an equation for the volume of the pyramid in terms of the base length b, we first express the height h as h = 2b + 201.
The volume V of a pyramid is given by the formula V = (1/3) × base area × height. Since the base of the pyramid is a square with side length b, the area of the base is b². Thus, substituting h into the volume formula and using b² for the base area, we get:
V = (1/3) × b² × (2b + 201)
Expanding this, we have:
V = (1/3) × b² × 2b + (1/3) × b² × 201
V = (2/3) × b³ + 67 × b²
Therefore, the equation for the volume of the pyramid in terms of the base length b is V = (2/3) × b³ + 67 × b².