**Middle School Number Sense Lesson 65: Rectangular Prisms**

In previous lessons, we have already looked at two different types of three-dimensional objects:

**Polyhedron**and

**Sphere**. Today we will focus on

**rectangular prisms**. Questions with this concept appeared

**7 times**last year on middle school tests, with a median placement at

**question # 67**.

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Think of a

**rectangular prism**as a

**box**. The following properties exist for each rectangular prism:

- Each face is a rectangle.
- Opposite faces are equal.
- All angles of each face are right angles.
- Adjacent faces meet at right angles.

**Formulas:**

- If the dimensions of a rectangular prism are
and**a**,**b**,**c****volume**is**abc**. - Its
**surface area**is**2ab + 2ac + 2bc**, or**2(ab + ac + bc)**.

**Example 1: What is the volume of a rectangular box that measures 2 by 4 by 5? ___**

- Use the formula
**abc**. - 2 x 4 x 5 =
**40**.

Example 2: What is the surface area of a rectangular prism with a base measuring 6 x 4, and a height of 3.5? ___

Example 2: What is the surface area of a rectangular prism with a base measuring 6 x 4, and a height of 3.5? ___

- Use the formula
**2(ab + ac + bc)**. - 2[(6 x 4) + (6 x 3.5) + (4 x 3.5)] = 2(24 + 21 + 14) = 2(59) =
**118**.

Example 3: What is the volume of a rectangular solid with dimensions: 20 by 12 by 4 inches? ___ cubic inches

Example 3: What is the volume of a rectangular solid with dimensions: 20 by 12 by 4 inches? ___ cubic inches

- Use the formula
**abc**. - 20 x 12 x 4 =
**960**.

**Example 4: The total surface area of a 3" by 4" by 5" rectangular prism is ___ square inches**

- Use the formula
**2(ab + ac + bc)**. - 2[(3 x 4) + (3 x 5) + (4 x 5)] = 2(12 + 15 + 20) = 2(47) =
**94**.

**Example 5: * Estimate: Find the volume of a rectangular prism with a square base measuring 45 x 45 inches, and a height of 27 inches. ___ cubic inches**

- Use the formula
**abc**. - 45 x 45 =
**2025**. Round this down to**2000**. - 2000 x 27 =
**54000**. - The exact answer is
**54675**, and the acceptable (+/- 5%) range is**from 51942 to 57408**.

**Example 6: * Estimate: Find the surface area of a rectangular prism with measure 25 by 30 by 35. ___**

- Use the formula
**2(ab + ac + bc)**. - 2(25 x 30) = 2(750) =
**1500**. - 2(25 x 35) is about 2(30 x 30) = 2(900) =
**1800**. - 2(30 x 35) = 2(1050) =
**2100**. - 1500 + 1800 + 2100 =
**5400**. - The exact answer is
**5350**, and the acceptable (+/- 5%) range is**from 5083 to 5617**.

**Check back soon for a free worksheet to help you practice Prism.**

**Up Next for Middle School: SlopeLineEqua**