Three-dimensional (3D) shapes are solid shapes that take up space.
They have three dimensions: height, width, and depth.
The space taken up by a three-dimensional shape is called volume.
Each of these 3D shapes has a volume.
In this lesson, let's learn how to find the volume of a cube and a rectangular prism.
Cubes have a height, width, and depth.
When we measure the volume of a cube or rectangular prism, we are actually measuring the number of cubic units that can fit in it.
A cubic unit is 1 unit high, 1 unit wide, 1 unit deep.
Tip: Cubic sounds like cube. They mean almost the same thing.
When we put cubic units together, we can create a cube or a rectangular prism.
How many cubic units fit inside this shape?
Let's count.
This shape has 16 cubic units in it.
When measuring larger shapes, it might be hard to measure volume by counting the cubic units one at a time.
We use a formula instead. 🧙♂️
Volume = Width × Height × Depth
Tip: This volume formula is only for cubes and rectangular prism.
What's the volume of this cube?
Let's multiply the width, height, and depth to find out:
Volume = 8 × 8 × 8
To multiply 3 factors, we just multiply any two at a time first.
8 × 8 = 64
Then, we multiply this answer by 8.
64 × 8 = 512
The volume of this cube is 512 cubic centimeters. ✅
Cubic centimeters is a unit of volume. It can also be written as cm3.
Let's find the volume of this rectangular prism together.
We multiply the height, width, and depth.
Volume = Width × Height × Depth
Let's put in the correct numbers into our formula.
Volume = 9 × 5 × 3
Multiply the first two numbers.
5 × 9 = 45
Now we multiply this answer by the third number.
45 × 3 = 135
The volume of our rectangular prism is 135 cubic inches. ✅
Cubic inches can also be written as in3. It's a unit of volume equal to a cube with 1 inch long sides.
Tip: Always write the unit of measurement after the number.
You just learned how to find the volume of two types of 3D shapes. Awesome!
Now, try the practice.