10A Volume Study Guide | Neft Teacher

Key Vocabulary

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

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

Length — how long the shape is. (largo)

Width — how wide the shape is. (ancho)

Height — how tall the shape is. (altura)

Cubic Units — the unit for measuring volume (cm³, in³, ft³). (unidades cúbicas)

Visual — Rectangular Prism

        +----------+
       /|         /|
      / |        / |  height (h) = 3 cm
     +----------+  |
     |  |       |  |
     |  +-------|--+
     | /        | /   width (w) = 4 cm
     |/         |/
     +----------+
      length (l) = 5 cm

  V = l × w × h = 5 × 4 × 3 = 60 cm³

Step-by-Step: Finding Volume

1 Identify the length, width, and height of the rectangular prism.
2 Multiply length × width × height.
3 Write the answer in cubic units (cm³, in³, ft³, etc.).

Formula Box

V = l × w × h

V = B × h (where B = area of the base)

Both formulas give the same answer. B = l × w (the area of the bottom face).

Watch Out!

Volume is in CUBIC units (cm³, in³). Area is in SQUARE units (cm², in²). Don't mix them up!
Make sure all measurements use the same unit before multiplying.
A cube is a special rectangular prism where l = w = h. Volume of a cube = s³.
Volume measures the INSIDE space, not the surface.

Practice Problems

1. Find the volume of a rectangular prism with length = 6 cm, width = 3 cm, height = 4 cm.

2. A box is 10 in long, 5 in wide, and 8 in tall. What is its volume?

3. A cube has sides of 7 cm. What is its volume?