Final answer:
The volume of a regular pyramid depends on the area of its base and its height using the formula V = (1/3)Ah, while the volume of a right cone is calculated with V = (1/3)πr²h. Consistent units must be used, and decimal answers should be rounded to the nearest hundredth.
Step-by-step explanation:
Finding the Volume of Pyramids and Cones
To find the volume of a regular pyramid with a square or equilateral triangular base, we can use the formula V = (1/3)Ah, where A is the area of the base and h is the height of the pyramid. For a pyramid with a square base, A would be the length of a side squared, and for a pyramid with an equilateral triangular base, A would be √3 / 4 times the length of a side squared. To find the volume of a right cone, the formula V = (1/3)πr²h is used, where r is the radius of the base and h is the height of the cone.
For both solids, the process involves finding the area of the base and then multiplying by the height, followed by multiplying the result by 1/3, as per the volume formulas. It is important to ensure that all units are consistent throughout the calculation process. For example, if the sides of a square base are provided in meters, the height should also be in meters for the volume to be in cubic meters. When calculating, round decimal answers to the nearest hundredth to maintain precision.