**High School Number Sense Lesson 106: Converting Distance Units with Volume--3 Dimensions**

This concept is an extension of

**ConvDistArea**. So far, I have only seen problems with English unit conversions (as opposed to metric unit conversions). It appeared

**3 times**this year, only on high school tests, with a median placement at

**question # 15**.

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**How to Solve:**

- Decide which direction you’re converting. If you are converting from a larger unit to a smaller one,
**multiply**. If going from a smaller unit to a larger one,**divide**. - Multiply or divide (as determined above) by the conversion factor,
**3 times**—once for each dimension.

**Example 1: 9 ft x 6 ft x 3 ft = ___ cubic yards**

- We are converting to a larger unit, so we will divide
- There are 3 feet in a yard, so we will divide by 3, three times.
- 9 ÷ 3 =
**3**. 6 ÷ 3 =**2**. 3 ÷ 3 =**1**. - Now multiply: 3 x 2 x 1 =
**6**.

**Example 2: 2 cubic feet = ___ cubic inches**

- We are converting to a smaller unit, so we will multiply.
- There are 12 inches in a foot, so we will multiply by 12, three times.
- 123 = 1728. 2 x 1728 =
**3456**.

**Example 3: 18” x 24” x 30” = ___ cubic feet**

- We are converting to a larger unit, so we will divide—in this case, by 12 (3 times).
- 18 ÷ 12 =
**3/2**. 24 ÷ 12 =**2**. 30 ÷ 12 =**5/2**. - Now multiply: 3/2 x 2 x 5/2 = 3 x 5/2 =
**15/2**.

**Example 4: 1/3 yard x 3 yards x 2 yards = ___ cu. ft.**

- We are converting to a smaller unit, so we will multiply—in this case, by 3 (3 times).
- 1/3 x 3 =
**1**. 3 x 3 =**9**. 2 x 3 =**6**. - Now multiply: 1 x 9 x 6 =
**54**.

**Example 5: 12 ft x 6 ft x 4 ft = ___ cubic yards**

- We are converting to a larger unit, so we will divide—in this case, by 3 (3 times).
- 12 ÷ 3 =
**4**. 6 ÷ 3 =**2**. 4 ÷ 3 =**4/3**. - Now multiply: 4 x 2 x 4/3 =
**32/3**.

**Example 6: 2 cubic yards = ___ cubic feet**

- We are converting to a smaller unit, so we will multiply—in this case, by 3 (3 times).
- 2 x 3 x 3 x 3 =
**54**.

**Up Next for High School: SetsUnion+Int**