5th Grade Volume of Rectangular Prisms Lesson (Free PDF)
Volume is the amount of space inside a solid figure, measured in cubic units. For a rectangular prism, multiply length times width times height: V = l × w × h. You can also multiply the area of the base by the height: V = B × h. For a solid made of two prisms, add the two volumes.
Grade 5 · Common Core State Standards: 5.MD.C.3, 5.MD.C.4, 5.MD.C.5
- A unit cube has volume 1 cubic unit.
- Volume is measured in cubic units such as cm³, in³ and ft³.
- V = l × w × h, and V = B × h where B is the base area.
- A composite solid made of two prisms has volume equal to the sum of the two volumes.
- Volume = (cubes in one layer) × (number of layers).
What is volume?
Volume is the amount of space inside a solid figure. We measure it by counting unit cubes. A unit cube has edges that are 1 unit long, so its volume is 1 cubic unit. If the edges are 1 centimeter long, the volume is 1 cubic centimeter, written \(1\text{ cm}^{3}\).
Volume: space inside a solid. Cubic unit: the volume of a cube with edge length 1. Base: the face the prism sits on. Layer: one level of unit cubes.
How do you find volume by counting cubes?
Fill the bottom layer, then count how many layers are stacked. This prism has 4 cubes along the length and 3 along the width, so one layer has \(4\times3=12\) cubes. There are 2 layers, so the volume is \(12\times2=24\) cubic units. Counting layers is the same as multiplying: the cubes in one layer tell the area of the base, and the number of layers tells the height. This idea lets you find the volume of a big box without building it.
What formulas give the volume of a rectangular prism?
Multiply the three edge lengths: \(V=l\times w\times h\). The product \(l\times w\) is the area of the base, so you can also write \(V=B\times h\), where \(B\) is the area of the base. Always check the unit. Edges measured in feet give a volume in cubic feet, written \(\text{ft}^{3}\). Mixing units, such as inches and feet in one product, gives a wrong answer, so change them to the same unit first.
How do you find the volume of a composite solid?
Split the solid into two rectangular prisms, find each volume, then add. Prism A is \(4\times3\times3=36\) and prism B is \(2\times3\times1=6\), so the whole solid is \(36+6=42\) cubic units. You can cut the solid a different way and still get the same total.
- Decide whether the solid is one prism or two.
- Find the length, width and height of each prism.
- Multiply to find each volume, with the right cubic unit.
- Add the volumes if there are two prisms.
Questions about volume of rectangular prisms
What is the difference between area and volume?
Area measures a flat surface in square units. Volume measures the space inside a solid in cubic units. A rectangle has area, but a box has volume because it has height as well.
Why do we use cubic units for volume?
Volume counts how many unit cubes fill a solid. Each cube has length, width and height of 1 unit, so the answer is in cubic units such as cubic feet or cm³.
How do I find a missing height?
Use V = l × w × h and divide the volume by the area of the base. For V = 90 and a 6 by 5 base, the base area is 30, and \(90 \div 30 = 3\).
What does V = B × h mean?
B is the area of the base and h is the height. The base area tells how many unit cubes fit in the bottom layer, and the height tells how many layers there are.
How do I find the volume of an L-shaped solid?
Cut the solid into two rectangular prisms. Find the volume of each by multiplying length, width and height, then add the two volumes together.
All Grade 5 chapters: Grade 5 math.
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