**High School Number Sense Lesson 86: Cubes (Solid)**

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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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:

*** V**= s

^{3}

*** SA**= 6s

^{2}

*** LSA**= 4s

^{2}

**Example 1: A cube with edge 2" has a surface area of ___ square inches**

- 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**

**Example 5:**

**The volume of a cube with a face area of 16 cm**

^{2}is ___ cm^{3}1. If the face area is 16, the edge is

**4**.

2. The volume is 4

^{3}, which is

**64**.

**Up Next for High School: TrigValue**