How to find the volume of a new box when doing prisms and pyramids
To find the volume of a prism or a pyramid, you need to know the dimensions of the shape. The formulas for finding the volume of a prism and a pyramid are slightly different, but both involve multiplying the base area of the shape by its height.
Here's how you can find the volume of a prism:
1. Determine the shape of the base. It can be any polygon, such as a rectangle, triangle, or hexagon.
2. Measure the dimensions of the base. For example, if the base is a rectangle, you need to know its length and width.
3. Calculate the area of the base by multiplying its length and width or using the appropriate formula for the specific shape of the base.
4. Measure the height of the prism. This is the perpendicular distance between the two bases.
5. Multiply the base area by the height to find the volume of the prism.
For example, if you have a rectangular prism with a base of length 4 cm and width 3 cm, and a height of 5 cm, you would calculate the volume as follows:
Base Area = length * width = 4 cm * 3 cm = 12 cm²
Volume = Base Area * height = 12 cm² * 5 cm = 60 cm³
Now, let's move on to finding the volume of a pyramid:
1. Determine the shape of the base. Like a prism, it can be any polygon.
2. Measure the dimensions of the base and calculate its area.
3. Measure the height of the pyramid, which is the perpendicular distance between the base and the apex (the top point of the pyramid).
4. Multiply the base area by the height and divide the result by 3 to find the volume of the pyramid.
For example, if you have a triangular pyramid with a base of length 6 cm, width 4 cm, and height 8 cm, you would calculate the volume as follows:
Base Area = (length * width) / 2 = (6 cm * 4 cm) / 2 = 12 cm²
Volume = (Base Area * height) / 3 = (12 cm² * 8 cm) / 3 = 32 cm³
So, with these steps, you can find the volume of a prism or a pyramid by calculating the base area and multiplying it by the height.