Final answer:
The formula V = 1/3Bh is for the volume of a cone and requires knowing the area of the base and the height. Formulas for the volumes of cylinders and spheres are similarly dimensionally consistent, while the formula V = 0.5bh lacks the 1/3 factor for a pyramid, and V = πd³/16 is not a typical volume formula.
Step-by-step explanation:
The question focuses on finding the volume of a solid using a given formula. The formula provided is for the volume of a cone, V = 1/3Bh, where B is the area of the base and h is the height of the solid. To use this formula, we must know the area of the base and the height. The area of the base for a circle (assuming the base is a circle) is calculated by A = πr², where r is the radius. This is dimensionally consistent, as A involves a length squared, which matches with the area's dimensions of length by length.
Comparing with the formulas provided in the reference, the formula for the volume of a sphere (V = 4/3 πr³) and the cylinder (V = πr²h) are also dimensionally consistent, as they involve a combination of lengths cubed, which is appropriate for volume. However, the expression V = 0.5bh, often used for the volume of a pyramid or triangle-based solid, is missing the 1/3 factor to be dimensionally accurate for a pyramid, and the expression V = πd³/16 does not seem to have a direct interpretation in terms of a common geometric shape. It's important to note the use of consistent units when calculating the volume as well.