We are all familiar with a cube (a.k.a. hexahedron), which is one of the five Platonic Solids covered in Polyhedron. Number sense tests will often have questions about a cube's volume or surface area. On high school tests, this concept appeared 9 times this year, with a median placement at question # 57.
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Number Dojo Level: 259
In terms of formulas, there aren't many to learn for cubes. A few abbreviations are helpful:
- V = volume
- s = side (or edge)
- SA = surface area
- LSA = lateral surface area (total surface area without the top and bottom faces)
Here are the formulas that have been needed for this year's questions:
- It helps me to visualize one face of the cube being a square, with area (2 x 2) = 4.
- Since there are 6 faces, the surface area is 6 x 4 = 24.
Example 2: The lateral surface area of a cube with edge length 3 inches is ___ sq. inches
- The area of one face of the cube is 3 x 3 = 9.
- The lateral surface area consists of the four vertical faces. 4 x 9 = 36.
Example 3: The volume of a cube is 15 cubic inches. If each side is doubled, the new volume is ___ cubic inches.
- This one requires a little bit of logic, since we can't calculate the cube root of 15 to find the length of one side. Instead, imagine a cube with edge length 1. Its volume is 1 x 1 x 1 = 1. Double the edge, and the volume becomes 2 x 2 x 2 = 8.
- Thus, doubling the side gives us 8 times the volume. 8 x 15 = 120.
Example 4: The edge of a cube with a lateral surface area of 9 sq. inches is ___ inches
- The area of one face will be 9/4.
- Take the square root to find the edge length: 3/2 or 1.5