A right rectangular prism is 3 cm by 6 cm by 8 cm. What is its volume
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Volume is the amount of space occupied by a three-dimensional object. In this lesson, we'll find the volume of a right rectangular prism with dimensions 3 centimeters by 6 centimeters by 8 centimeters. Volume is measured in cubic units, such as cubic centimeters.
A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. It has 8 vertices and 12 edges. The opposite faces of a rectangular prism are congruent. In our example, the dimensions are length 6 centimeters, width 3 centimeters, and height 8 centimeters.
The volume of a rectangular prism can be found by filling it with unit cubes. If we have a prism with length l, width w, and height h, we can fit l unit cubes along the length, w unit cubes along the width, and h unit cubes along the height. The total number of unit cubes is l times w times h. This gives us the volume formula: V equals length times width times height.
Now we'll apply the volume formula to our rectangular prism with dimensions 3 centimeters by 6 centimeters by 8 centimeters. We substitute these values into the formula V equals length times width times height. This gives us V equals 3 times 6 times 8 cubic centimeters. First, we multiply 3 by 6 to get 18 square centimeters. Then we multiply 18 by 8 to get 144 cubic centimeters. Therefore, the volume is 144 cubic centimeters.
We've calculated that the volume of our rectangular prism is 144 cubic centimeters. Because multiplication is commutative, we can multiply the dimensions in any order and still get the same result. For example, 3 times 6 times 8 equals 144, 6 times 8 times 3 equals 144, and 8 times 3 times 6 equals 144. This means we would need 144 unit cubes, each with a volume of 1 cubic centimeter, to completely fill this rectangular prism.
Let's practice with another example. Find the volume of a rectangular prism with dimensions 4 centimeters by 5 centimeters by 7 centimeters. Using the formula V equals length times width times height, we substitute the values to get V equals 4 times 5 times 7 cubic centimeters. First, we multiply 4 by 5 to get 20 square centimeters. Then we multiply 20 by 7 to get 140 cubic centimeters. Therefore, the volume is 140 cubic centimeters.