Volume of a Rectangular Prism
Grade 8 math lesson on calculating the volume of rectangular prisms using length times width times height. Students learn to identify the three dimensions of a prism, apply the volume formula, and solve real-world problems involving containers, storage, and capacity.
Key Concepts
Property For a rectangular prism, the volume ($V$) is the product of its length ($l$), width ($w$), and height ($h$). $$V = lwh$$.
Examples A classroom is 35 feet long, 25 feet wide, and 10 feet high. $V = lwh = (35 \text{ ft})(25 \text{ ft})(10 \text{ ft}) = 8750 \text{ ft}^3$. A shoebox has dimensions of 14 inches by 8 inches by 5 inches. $V = lwh = (14 \text{ in})(8 \text{ in})(5 \text{ in}) = 560 \text{ in}^3$.
Explanation This is a special version of the prism formula made just for boxy shapes! Since the base of a rectangular prism is a rectangle, its area ($B$) is simply length times width ($l \times w$). So, we can swap $B$ for $lw$ to get a fast and easy formula for anything from a classroom to a cereal box.
Common Questions
How do you find the volume of a rectangular prism?
Volume of a rectangular prism = length x width x height. Multiply all three dimensions together to get the volume in cubic units. For example, a box that is 5 x 3 x 4 cm has volume = 60 cubic centimeters.
What is volume and why is it measured in cubic units?
Volume is the amount of three-dimensional space a solid occupies. It is measured in cubic units because we count how many unit cubes fit inside the shape. A cubic centimeter is a 1x1x1 cm cube.
How do you find a missing dimension when you know the volume?
If volume = length x width x height, divide the volume by the two known dimensions to find the missing one. For example, if volume = 120, length = 5, width = 4: height = 120 / (5 x 4) = 6.
What are real-world examples of volume of rectangular prisms?
Volume calculations are used to find how much water a fish tank holds, how much soil to buy for a garden bed, how many boxes fit in a shipping container, and the capacity of storage rooms.