Surface Areas and Volumes Class 10 Maths — Revision Notes
This chapter covers surface area and volume formulas for 3D shapes like cubes, cylinders, cones, and spheres. Students learn applications in real-world pro
TL;DR: This chapter covers surface area and volume formulas for 3D shapes like cubes, cylinders, cones, and spheres. Students learn applications in real-worl…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter covers surface area and volume formulas for 3D shapes like cubes, cylinders, cones, and spheres. Students learn applications in real-world pro
Surface Area Formulas
- Cube: SA = 6a^2 where a is side length
- Cylinder: SA = 2πrh + 2πr^2 (lateral + two circular bases)
- Cone: SA = πrl + πr^2 where l is slant height
- Sphere: SA = 4πr^2
Volume Formulas
- Cube: V = a^3
- Cylinder: V = πr^2h
- Cone: V = 1/3 πr^2h
- Sphere: V = 4/3 πr^3
Combined Shapes
- Hemisphere: SA = 2πr^2 (curved) + πr^2 (base), V = 2/3 πr^3
- Composite shapes: find volume by adding/subtracting individual parts
- Example: cone on hemisphere = V cone + V hemisphere
- Surface area of composite: sum of exposed surfaces only
Applications
- Finding how many units of one shape fit into another
- Volume conservation: water from one shape poured into another
- Cost problems: finding cost of material for given surface area
- Capacity problems: maximum volume container can hold
Key Terms
- Surface Area: Total area of all surfaces of 3D shape
- Volume: Amount of space occupied by 3D shape
- Slant Height: Distance from apex to edge of base along surface of cone
Frequently Asked Questions
What is the formula for curved surface area of cylinder?
Curved surface area = 2πrh where r is radius and h is height. This is lateral surface area excluding the two circular bases.
How do you find volume of composite shape?
Identify the constituent 3D shapes. Calculate volume of each shape. Add volumes if shape is combination, subtract if one shape is removed from another.
More Class 10 Maths Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
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