📖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
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
Find the volume of a cube with side length 4 cm
Answer: 64 cm³
Find the volume of a cylinder with radius 3 m and height 5 m (use π = 3.14)
Answer: 141.3 m³
Find the volume of a sphere with radius 6 cm (use π = 3.14)
Answer: 904.32 cm³
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