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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>A frustum is a 3-dimensional shape that results from slicing the top off a cone parallel to its base. The surface area of a frustum includes the areas of its two circular bases and the curved surface that connects them. In this article, we will learn about the surface area of a frustum.</p>
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<p>A frustum is a 3-dimensional shape that results from slicing the top off a cone parallel to its base. The surface area of a frustum includes the areas of its two circular bases and the curved surface that connects them. In this article, we will learn about the surface area of a frustum.</p>
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<h2>What is the Surface Area of a Frustum?</h2>
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<h2>What is the Surface Area of a Frustum?</h2>
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<p>The surface area of a frustum is the total area occupied by its outer surfaces. It is measured in<a>square</a>units. A frustum is formed by cutting a cone parallel to its<a>base</a>, resulting in two parallel circular bases and a curved surface connecting them. Unlike a complete cone, a frustum does not have a vertex.</p>
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<p>The surface area of a frustum is the total area occupied by its outer surfaces. It is measured in<a>square</a>units. A frustum is formed by cutting a cone parallel to its<a>base</a>, resulting in two parallel circular bases and a curved surface connecting them. Unlike a complete cone, a frustum does not have a vertex.</p>
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<h2>Surface Area of a Frustum Formula</h2>
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<h2>Surface Area of a Frustum Formula</h2>
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<p>A frustum has a curved surface and two circular bases. The surface area of a frustum is the<a>sum</a>of the lateral surface area and the areas of the two bases. Look at the frustum below to see its surface area, height (h), slant height (l), and radii (R and r) of the two bases.</p>
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<p>A frustum has a curved surface and two circular bases. The surface area of a frustum is the<a>sum</a>of the lateral surface area and the areas of the two bases. Look at the frustum below to see its surface area, height (h), slant height (l), and radii (R and r) of the two bases.</p>
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<p>The surface area of a frustum is calculated as: Lateral Surface Area of a Frustum Total Surface Area of a Frustum</p>
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<p>The surface area of a frustum is calculated as: Lateral Surface Area of a Frustum Total Surface Area of a Frustum</p>
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<h2>Lateral Surface Area of a Frustum</h2>
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<h2>Lateral Surface Area of a Frustum</h2>
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<p>The lateral surface area of a frustum is the area of the curved surface connecting the two circular bases.</p>
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<p>The lateral surface area of a frustum is the area of the curved surface connecting the two circular bases.</p>
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<p>It is calculated using the<a>formula</a>: Lateral Surface Area = π(R + r)l square units</p>
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<p>It is calculated using the<a>formula</a>: Lateral Surface Area = π(R + r)l square units</p>
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<p>Here, R and r are the radii of the larger and smaller bases, respectively, and l is the slant height of the frustum.</p>
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<p>Here, R and r are the radii of the larger and smaller bases, respectively, and l is the slant height of the frustum.</p>
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<h2>Total Surface Area of a Frustum</h2>
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<h2>Total Surface Area of a Frustum</h2>
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<p>The total surface area of a frustum includes the lateral surface area and the areas of the two circular bases.</p>
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<p>The total surface area of a frustum includes the lateral surface area and the areas of the two circular bases.</p>
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<p>The total surface area is calculated using the formula:</p>
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<p>The total surface area is calculated using the formula:</p>
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<p>Total Surface Area = Lateral Surface Area + Area of Top Base + Area of Bottom Base = π(R + r)l + πR² + πr²</p>
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<p>Total Surface Area = Lateral Surface Area + Area of Top Base + Area of Bottom Base = π(R + r)l + πR² + πr²</p>
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<p>Where R and r are the radii of the larger and smaller bases, and l is the slant height of the frustum.</p>
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<p>Where R and r are the radii of the larger and smaller bases, and l is the slant height of the frustum.</p>
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<h2>Volume of a Frustum</h2>
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<h2>Volume of a Frustum</h2>
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<p>The volume of a frustum is the space enclosed within its surfaces. It can be found using the formula:</p>
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<p>The volume of a frustum is the space enclosed within its surfaces. It can be found using the formula:</p>
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<p>Volume = (1/3)πh(R² + r² + Rr) cubic units</p>
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<p>Volume = (1/3)πh(R² + r² + Rr) cubic units</p>
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<p>Where R and r are the radii of the larger and smaller bases, respectively, and h is the vertical height of the frustum.</p>
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<p>Where R and r are the radii of the larger and smaller bases, respectively, and h is the vertical height of the frustum.</p>
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<h2>Confusion between Lateral Surface Area and Total Surface Area</h2>
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<h2>Confusion between Lateral Surface Area and Total Surface Area</h2>
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<p>Students sometimes confuse the lateral surface area with the total surface area of a frustum. Remember, the lateral surface area only includes the curved surface, while the total surface area includes the curved surface and the two bases.</p>
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<p>Students sometimes confuse the lateral surface area with the total surface area of a frustum. Remember, the lateral surface area only includes the curved surface, while the total surface area includes the curved surface and the two bases.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Given R = 8 cm, r = 5 cm, l = 12 cm. Use the formula: Lateral Surface Area = π(R + r)l = 3.14 × (8 + 5) × 12 = 3.14 × 13 × 12 = 490.08 cm²</p>
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<p>Given R = 8 cm, r = 5 cm, l = 12 cm. Use the formula: Lateral Surface Area = π(R + r)l = 3.14 × (8 + 5) × 12 = 3.14 × 13 × 12 = 490.08 cm²</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Find the total surface area of a frustum with larger base radius 6 cm, smaller base radius 4 cm, and slant height 10 cm.</p>
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<p>Find the total surface area of a frustum with larger base radius 6 cm, smaller base radius 4 cm, and slant height 10 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Total Surface Area = 628.32 cm²</p>
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<p>Total Surface Area = 628.32 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Use the formula: Total Surface Area = π(R + r)l + πR² + πr² = 3.14 × (6 + 4) × 10 + 3.14 × 6² + 3.14 × 4² = 3.14 × 10 × 10 + 3.14 × 36 + 3.14 × 16 = 314 + 113.04 + 50.24 = 628.32 cm²</p>
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<p>Use the formula: Total Surface Area = π(R + r)l + πR² + πr² = 3.14 × (6 + 4) × 10 + 3.14 × 6² + 3.14 × 4² = 3.14 × 10 × 10 + 3.14 × 36 + 3.14 × 16 = 314 + 113.04 + 50.24 = 628.32 cm²</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>A frustum has a larger base radius of 7 cm, a smaller base radius of 3 cm, and a height of 9 cm. Find the total surface area.</p>
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<p>A frustum has a larger base radius of 7 cm, a smaller base radius of 3 cm, and a height of 9 cm. Find the total surface area.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Total Surface Area = 579.58 cm²</p>
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<p>Total Surface Area = 579.58 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>First, find the slant height using the Pythagorean theorem: l = √((R - r)² + h²) = √((7 - 3)² + 9²) = √(16 + 81) = √97 = 9.85 cm Use the formula: Total Surface Area = π(R + r)l + πR² + πr² = 3.14 × (7 + 3) × 9.85 + 3.14 × 7² + 3.14 × 3² = 3.14 × 10 × 9.85 + 3.14 × 49 + 3.14 × 9 = 309.41 + 153.86 + 28.26 = 579.58 cm²</p>
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<p>First, find the slant height using the Pythagorean theorem: l = √((R - r)² + h²) = √((7 - 3)² + 9²) = √(16 + 81) = √97 = 9.85 cm Use the formula: Total Surface Area = π(R + r)l + πR² + πr² = 3.14 × (7 + 3) × 9.85 + 3.14 × 7² + 3.14 × 3² = 3.14 × 10 × 9.85 + 3.14 × 49 + 3.14 × 9 = 309.41 + 153.86 + 28.26 = 579.58 cm²</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Find the lateral surface area of a frustum with larger base radius 10 cm, smaller base radius 6 cm, and slant height 8 cm.</p>
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<p>Find the lateral surface area of a frustum with larger base radius 10 cm, smaller base radius 6 cm, and slant height 8 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Lateral Surface Area = 402.12 cm²</p>
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<p>Lateral Surface Area = 402.12 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>Lateral Surface Area = π(R + r)l = 3.14 × (10 + 6) × 8 = 3.14 × 16 × 8 = 402.12 cm²</p>
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<p>Lateral Surface Area = π(R + r)l = 3.14 × (10 + 6) × 8 = 3.14 × 16 × 8 = 402.12 cm²</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The slant height of a frustum is 14 cm, its larger base radius is 9 cm, and its lateral surface area is 792 cm². Find the smaller base radius.</p>
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<p>The slant height of a frustum is 14 cm, its larger base radius is 9 cm, and its lateral surface area is 792 cm². Find the smaller base radius.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Smaller Base Radius = 7 cm</p>
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<p>Smaller Base Radius = 7 cm</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>It is the total area that covers the outside of the frustum, including its curved side and the two bases.</h2>
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<h2>It is the total area that covers the outside of the frustum, including its curved side and the two bases.</h2>
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<h3>1.What are the components of the surface area of a frustum?</h3>
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<h3>1.What are the components of the surface area of a frustum?</h3>
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<p>The surface area of a frustum includes the lateral surface area and the areas of the top and bottom bases.</p>
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<p>The surface area of a frustum includes the lateral surface area and the areas of the top and bottom bases.</p>
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<h3>2.What is the difference between slant height and height in a frustum?</h3>
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<h3>2.What is the difference between slant height and height in a frustum?</h3>
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<p>Slant height is the length of the side from the top edge to the bottom edge. Height is the perpendicular distance between the bases.</p>
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<p>Slant height is the length of the side from the top edge to the bottom edge. Height is the perpendicular distance between the bases.</p>
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<h3>3.Are lateral surface area and curved surface area the same in a frustum?</h3>
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<h3>3.Are lateral surface area and curved surface area the same in a frustum?</h3>
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<p>Yes, in a frustum, the lateral surface area and curved surface area refer to the same part.</p>
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<p>Yes, in a frustum, the lateral surface area and curved surface area refer to the same part.</p>
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<h3>4.What unit is surface area measured in?</h3>
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<h3>4.What unit is surface area measured in?</h3>
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<p>Surface area is always measured in square units like cm², m², or in².</p>
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<p>Surface area is always measured in square units like cm², m², or in².</p>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Frustum</h2>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Frustum</h2>
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<p>Students often make mistakes while calculating the surface area of a frustum, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.</p>
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<p>Students often make mistakes while calculating the surface area of a frustum, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.</p>
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<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
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<h2>Seyed Ali Fathima S</h2>
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<h2>Seyed Ali Fathima S</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
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<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She has songs for each table which helps her to remember the tables</p>
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<p>: She has songs for each table which helps her to remember the tables</p>