Surface Areas and Volumes 10 Maths — Revision Notes
Surface area and volume are measurements of 3D shapes essential for solving practical problems. Understanding formulas for various shapes enables calculati
TL;DR: Surface area and volume are measurements of 3D shapes essential for solving practical problems. Understanding formulas for various shapes enables calc…
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Surface area and volume are measurements of 3D shapes essential for solving practical problems. Understanding formulas for various shapes enables calculati
Surface Area Formulas
- Cube: SA = 6a² where a is side length
- Rectangular prism: SA = 2(lw + wh + lh)
- Sphere: SA = 4πr²
- Cylinder: SA = 2πr² + 2πrh
- Cone: SA = πr² + πrl where l is slant height
Volume Formulas
- Cube: V = a³
- Rectangular prism: V = l × w × h
- Sphere: V = 4/3 πr³
- Cylinder: V = πr²h
- Cone: V = 1/3 πr²h
Hemisphere and Combination Shapes
- Hemisphere surface area: 3πr² (curved surface + flat base)
- Hemisphere volume: 2/3 πr³
- Combined shapes: break into component parts and add volumes/areas
Applications and Problem Solving
- Conversion between units (cm³ to liters, etc.)
- Calculating material needed for construction
- Finding dimensions from given surface area or volume
- Problems involving composite figures made of multiple shapes
Key Terms
- Surface Area: Total area of all surfaces of 3D shape
- Volume: Space occupied by 3D shape
- Lateral Surface Area: Area of curved/side surfaces excluding bases
- Slant Height: Distance from apex to base edge along surface of cone/pyramid
- Hemisphere: Half of a sphere
Frequently Asked Questions
What is the volume of sphere with radius 3 cm?
Using V = 4/3 πr³: V = 4/3 π(3)³ = 4/3 π × 27 = 36π cm³ ≈ 113.1 cm³.
How do you find slant height of cone if radius and height are known?
Using Pythagorean theorem: l = √(r² + h²).
What is the difference between surface area and volume?
Surface area measures area of all surfaces (square units); volume measures space inside (cubic units).
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