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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

📐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

Identify the 3D Shape

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

Find Required Measurements

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

Apply the Correct Formula

Use the appropriate formula for the shape.

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

Printable Volume practice

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Worked Examples

Volume of Rectangular Prism Exampleeasy

Area Surface Area Circles 3D Shapes

Curriculum Alignment

CommonCore (5.MD.C.5)KS3KMK

Classroom assessment context

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