Assignment: 10-Volume
Practice: 11-Surface Area and Volume Practice
Once you are familiar with area, volume comes a bit easier. There is just one simple formula.
V = B x h
Notice, I used a capital B. This represents the area of the base of a three-dimensional figure. It is the large B to differentiate it from the base of a two-dimensional figure, which we would write as b. The differentiation is necessary when dealing with things the volume of a triangular prism. Remember, the formula for area of a triangle is a = bh/2. You don’t want to confuse your B, for area of the base of the prism, with the little b, for the length of the base of the triangle. Let’s begin by looking at a cube.
The base of a cube is a square. To find the area of that square, you do length times width, which would be 4 x 4 = 16 in². To finish the formula for volume, we multiply that by the height, which being a cube is also 4: 16 x 4 = 64 in³. Notice the units are now cubed. This is because we are dealing with all three dimensions: width, height, and depth.
Next, let’s look our rectangular prism again, except this time, let’s find the volume of it.
The base of a rectangular prism is a rectangle. Really, you could choose any of the rectangles to start with. For consistency, let’s start with B. Remember, the area of B was 8 x 3 = 24 in². We would then multiply that by the remaining dimension of 5: 24 x 5 = 120 in³.
The final shape we will have to worry about finding the volume of this year is the triangular prism.
The base of a triangular prism is the triangle. To find the area of that triangle, we would do 3.5 x 4 / 2 = 7 in². We then multiply that by the height: 7 x 6= 42 in³.