A right rectangular prism is 3 cm by 5 cm by 7 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 5 centimeters by 7 centimeters.
A right rectangular prism, also known as a rectangular box or cuboid, has six rectangular faces, twelve edges, and eight vertices. Our specific prism has dimensions of 3 centimeters by 5 centimeters by 7 centimeters. These represent the length, width, and height of the prism.
Volume can be found by counting how many unit cubes fit inside the prism. A unit cube has dimensions 1 by 1 by 1. For our prism, we can fit 3 unit cubes along the length, 5 along the width, and 7 along the height. The total number of unit cubes is 3 times 5 times 7, which gives us the volume formula: Volume equals length times width times height.
Now let's calculate the volume of our rectangular prism. We start with the formula: Volume equals length times width times height. Substituting our values: Volume equals 3 centimeters times 5 centimeters times 7 centimeters. First we calculate 3 times 5, which equals 15. Then we multiply 15 by 7, giving us 105. Since we're multiplying three lengths measured in centimeters, our final unit is cubic centimeters. Therefore, the volume is 105 cubic centimeters.
Let's verify our answer visually. If we had 105 unit cubes, they would perfectly fill our 3 by 5 by 7 rectangular prism. We can also verify our calculation using different multiplication orders. First, we could calculate 3 times 7 equals 21, then multiply by 5 to get 105. Alternatively, we could calculate 5 times 7 equals 35, then multiply by 3 to also get 105. This confirms that multiplication order doesn't affect the result, thanks to the commutative property.
Calculating rectangular prism volume has many practical applications. For example, determining the storage capacity of boxes helps with packaging and shipping. Calculating the volume of concrete needed for building foundations ensures structural integrity. Finding the water capacity of rectangular tanks is essential for water management. Our 105 cubic centimeter prism could represent any of these real-world objects, scaled appropriately. Remember to always include the correct units in your volume measurements.