5C Volume of Rectangular Prisms Study Guide

Key Vocabulary

Volume — the amount of space inside a 3D shape, measured in cubic units. (volumen)

Rectangular Prism — a 3D shape with 6 rectangular faces (like a box or brick). (prisma rectangular)

Base Area — the area of the bottom face of the prism (B = l × w). (área de la base)

Cubic Units — units used to measure volume (cm³, in³, ft³). (unidades cúbicas)

Capacity — the amount a container can hold. (capacidad)

Visual — Prism with Fractional Dimensions

        +----------+
       /|         /|
      / |        / |  height = 4 in
     +----------+  |
     |  |       |  |
     |  +-------|--+
     | /        | /   width = 2 in
     |/         |/
     +----------+
      length = 3½ in

  V = 3½ × 2 × 4
  V = 7/2 × 2 × 4
  V = 7 × 4 = 28 in³

Step-by-Step: Volume with Fractions

1 Identify the length, width, and height. Check for fractions!
2 Convert mixed numbers to improper fractions if needed (e.g., 3½ = 7/2).
3 Multiply length × width × height.
4 Simplify the answer and write in cubic units.

Example: l = 2½, w = 1½, h = 3
Convert: 5/2 × 3/2 × 3
= (5 × 3 × 3) / (2 × 2) = 45/4 = 11¼ cubic units

Formula Box

V = l × w × h

V = B × h (B = area of the base)

Works for whole numbers AND fractions!

Watch Out!

Fractional edges: Convert mixed numbers to improper fractions BEFORE multiplying.
Multiply fractions carefully: Multiply numerators together, then denominators together.
Units are CUBED: If the sides are in inches, volume is in in³ (cubic inches).
Don't confuse area and volume. Area = 2 dimensions (square units). Volume = 3 dimensions (cubic units).

Practice Problems

1. Find the volume: l = 3½ in, w = 2 in, h = 4 in.

2. Find the volume: l = 6 cm, w = 5 cm, h = 3 cm.

3. Find the volume: l = 4 ft, w = 2½ ft, h = 2 ft.