Grade 6 (age 11-12)

grade 6 Volume of Space Figures

Volume of Space Figures

Volume is how much space an object takes up. Count how many one-centimeter cubes fit along the length, the width, and each layer, and the total is the volume, which is why a box equals length times width times height. The 1 L on a milk carton equals 1000 cubic centimeters, so stack cubes and change the dimensions to see how the volume is set. Grade 5 already had length×width×height and surface area. This chapter recounts with cubes and converts cm³ to L.

Understand Volume with Cubes

🧱 Stack 1-Unit Blocks!

①One unit cube = 1 cm³

②Count rows, columns, and layers

③Total = length × width × height = volume!

Layers3

Per row3

Volume of a Box

Length5

Width3

Height4

📦 Box = Length × Width × Height

①Count blocks on the base (length × width)

②Stack as many layers as the height

③Cube: all sides equal → side³

This box now

5 × 3 × 4 = 60 cm³ = 0.06 L

Length, width, and height from the sliders above. Convert with 1000 cm³ = 1 L.

Volume Units

🥛 1 L = 1000 cm³

①1 cm³ = volume of a 1-cm cube

②1 L = 10 × 10 × 10 = 1000 cm³

③1 L milk carton: length × width × height = 1000 cm³

Summary

Volume of a Box

V = Length × Width × Height

Base area × height = L × W × H

Volume of a Cube

V = a³ (side × side × side)

All edges equal

Volume Units

1 L = 1000 cm³ = 1000 mL

10 × 10 × 10 cm = 1000 cm³ = 1 L

🎯 Key Points

①Volume = space occupied

②Box: L × W × H

③Cube: side³

④Units: 1 L = 1000 cm³ = 1000 mL

⑤Verify by counting unit cubes!

Examples & Unit Review

Example 1

Find the volume of a rectangular prism that is 6 cm by 4 cm by 5 cm.

Volume of a rectangular prism = length × width × height = 6 × 4 × 5.

24 × 5 = 120, so 120 cm³.

▸ 120 cm³

The volume of a rectangular prism is the base (length × width) times the height.

Example 2

A cube has an edge of 5 cm. What is its volume in cm³, and how many liters is that?

Volume of a cube = edge × edge × edge = 5 × 5 × 5 = 125 cm³.

Since 1 L = 1000 cm³, 125 cm³ = 0.125 L.

▸ 125 cm³ = 0.125 L

A cube has equal edges, so its volume is the edge multiplied three times.

Unit Review

A cube measures 10 cm by 10 cm by 10 cm. What is its volume in liters?

①1 L

②10 L

③100 L

④0.1 L

▸ ① 1 L

Volume = 10 × 10 × 10 = 1000 cm³.

Since 1 L = 1000 cm³, 1000 cm³ = 1 L.

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Cylinder, Cone, Sphere

Prisms and Pyramids