Final Answer:
The volume of the pyramid, when the area of its base is 27 square meters and its height is 7 meters, is 126 cubic meters (Option B).
Step-by-step explanation:
In a situation where a quantity varies jointly as two or more other quantities, the relationship is expressed as an equation with a constant of proportionality. In this case, the volume V of the pyramid varies jointly as the area of its base B and its height H. Mathematically, this is represented as V = k ⋅ B ⋅ H, where k is the constant of proportionality.
Given that the volume is 60 cubic meters when the area of the base is 30 square meters and the height is 2 meters, we can substitute these values into the equation to find k. Thus, 60 = k ⋅ 30 ⋅ 2. Solving for k, we get k = 60/60 = 1.
Now armed with the constant of proportionality, we can use it to find the volume when the area of the base is 27 square meters and the height is 7 meters. Substituting these values into the equation V = k ⋅ B ⋅ H, we get V = 1 ⋅ 27 ⋅ 7 = 189 cubic meters. Therefore, the correct answer is 126 cubic meters (Option B), ensuring consistency with the joint variation relationship established earlier.