What Is the Volume?(With Examples)

Volume is the amount of three-dimensional space inside a solid shape. It measures how much space an object takes up or how much it can hold. Volume is measured in cubic units (cm³, m³, in³, ft³, liters, etc.).

Grades 5-8Key Stage 3 (Year 7-9)Årskurs 6-9Klasse 6-9

📖Definition

Volume is the amount of three-dimensional space inside a solid shape. It measures how much space an object takes up or how much it can hold. Volume is measured in cubic units (cm³, m³, in³, ft³, liters, etc.).

📐Formula

Cube: V = s³; Prism: V = Bh; Cylinder: V = πr²h; Sphere: V = (4/3)πr³

For prisms and cylinders, multiply the base area by the height. For cubes, cube the side length. For spheres, use (4/3) times pi times radius cubed.

📝Step-by-Step Guide

1

Identify the 3D Shape

Determine if it's a cube, prism, cylinder, cone, sphere, or other solid.

2

Find Required Measurements

Identify the dimensions needed: side length, radius, height, or base area.

3

Apply the Correct Formula

Use the appropriate formula for the shape.

4

Use Cubic Units

Always express volume in cubic units (cm³, m³, etc.).

⚠️Common Mistakes to Avoid

  • Using square units instead of cubic units
  • Confusing volume with surface area
  • Using diameter instead of radius
  • Forgetting to cube the units
  • Not using the correct formula for the shape

✏️Practice Problems

Easy

Find the volume of a cube with side length 4 cm

Answer: 64 cm³

Medium

Find the volume of a cylinder with radius 3 m and height 5 m (use π = 3.14)

Answer: 141.3 m³

Hard

Find the volume of a sphere with radius 6 cm (use π = 3.14)

Answer: 904.32 cm³

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Worked Examples

Curriculum Alignment

CommonCore (5.MD.C.5)KS3KMK