Surface Areas And Volumes Formulas - Mathematics Class 10

Learn important formulas from the Surface Areas And Volumes chapter of Class 10 Mathematics with examples, variables and applications.

📐 Surface Areas And Volumes Formulas

Complete collection of formulas with explanations and examples

Surface Area of Sphere

$$SA = 4 pi r^2$$

Description: Surface Area of Sphere is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: SA = 4 pi r^2

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

TSA of Cube

$$TSA = 6a^2$$

Description: TSA of Cube is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: TSA = 6a^2

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Volume of Cone

$$V = 1/3 pi r^2 h$$

Description: Volume of Cone is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: V = 1/3 pi r^2 h

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Volume of Cube

$$V = a^3$$

Description: Volume of Cube is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: V = a^3

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Volume of Cylinder

$$V = pi r^2 h$$

Description: Volume of Cylinder is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: V = pi r^2 h

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Volume of Sphere

$$V = 4/3 pi r^3$$

Description: Volume of Sphere is a standard relation used in surface-areas-and-volumes.

Example:

Apply the relation: V = 4/3 pi r^3

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Quick Reference

Surface Area of Sphere: $SA = 4 pi r^2$
TSA of Cube: $TSA = 6a^2$
Volume of Cone: $V = 1/3 pi r^2 h$
Volume of Cube: $V = a^3$
Volume of Cylinder: $V = pi r^2 h$
Volume of Sphere: $V = 4/3 pi r^3$

💡 Worked Examples

Step-by-step solutions using Surface Areas And Volumes formulas

Example 1: Area of Circle

Circle Area Formula
Problem:

Find the area of a circle with radius 7 cm.

Solution:
  1. Given: r = 7 cm
  2. Apply formula: A = πr²
  3. Substitute: A = π × 7²
  4. Calculate: A = π × 49 = 49π cm²
  5. Approximate: A ≈ 49 × 3.14159 ≈ 153.94 cm²
Answer:

Area = 49π cm² ≈ 153.94 cm²

🎯 Practice Problems

Try these problems to test your understanding:

Practice Problem 1

Solve the quadratic equation: x² - 7x + 12 = 0

Practice Problem 2

Find the area of a circle with diameter 14 cm.

Practice Problems

Check Your Formula Recall

Write each formula once, define every variable, then solve one direct substitution problem before moving to mixed questions.

Apply Surface Areas And Volumes

Pick two formulas from this page and create your own values for the variables. Verify units and signs before calculating.

Derivation Notes

Focus on how the formula is built, not only the final expression. Derivations help with board-exam reasoning and multi-step application questions.

  • Start from the definition or identity used in the chapter.
  • Write assumptions clearly before substituting values.
  • Track units through each step to catch calculation mistakes.

Where These Formulas Are Used

Board Exam Problems

Use these formulas for direct numerical questions, proof-based steps, and short-answer reasoning in Mathematics.

Competitive Practice

Memorize the condition of use for each formula so you can identify the right expression quickly under timed practice.

Related Formula Chapters

Applications Of Trigonometry 1 formulas Areas Related To Circles 4 formulas Arithmetic Progressions 2 formulas Coordinate Geometry 3 formulas Pair Of Linear Equations 3 formulas Polynomials 2 formulas Quadratic Equations 2 formulas Real Numbers 1 formulas Statistics And Probability 4 formulas Surface Areas And Volumes 6 formulas Triangles 1 formulas Trigonometry 5 formulas

These Surface Areas And Volumes formulas help students revise concepts quickly and apply equations accurately in exam-style problems.

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