Discovering Volume

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Understanding volume can be a tricky topic because it is easy to get it confused with area and perimeter. There are some main things that can help you understand volume. First, you want to make sure that all of the dimensions are labeled in cubic units. For example, if you have a triangular prism with sides measured in centimeters, you want the answer to be in cubic centimeters. Secondly, there are separate formulas to find the volume of a prism and the volume of a pyramid. Thirdly, you want to know the shape or 3 dimensional object you are dealing with because that will help you to determine the formula you need to use. Let’s look at some examples!

The formula for a prism is V = Area of base x height of prism. A prism is a three-dimensional shape with two parallel bases that are the same. In the picture below I have drawn a right prism. The base in this case is the square; therefore, area = length x width (3cm x 3cm = 9cm squared). Once we find the area of the base, we need to multiply it by the height of the prism (5 cm). The answer to the example is 45cm cubed because 45 cm cubed = 9 cm squared x 5 cm.

The formula for a pyramid is V = 1/3 x Area of base x height of pyramid. A pyramid is a three-dimensional shape with one base of any shape with sides all meeting at one point. In the picture above I have drawn a triangular pyramid. The one base in the pyramid is a triangle; therefore, area = 1/2 length x height (1/2 x 4 cm x 8 cm= 16 cm squared). Once we find the area of the base, we need to multiply it by the height of the pyramid which in the example is 10 cm. Lastly, we multiply the whole answer by 1/3. The answer to the example is about 53.3 cm cubed. The descriptions above can help clear up any confusion, and help to explain the two different formulas for volume of a prism and the volume of a pyramid.

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