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2026-01-01
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<p>Last updated on<strong>September 4, 2025</strong></p>
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<p>Last updated on<strong>September 4, 2025</strong></p>
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<p>A torus is a 3-dimensional shape that resembles a doughnut, featuring a circular path that revolves around an axis in its plane. The surface area of a torus is the total area covered by its outer surface. In this article, we will learn about the surface area of a torus.</p>
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<p>A torus is a 3-dimensional shape that resembles a doughnut, featuring a circular path that revolves around an axis in its plane. The surface area of a torus is the total area covered by its outer surface. In this article, we will learn about the surface area of a torus.</p>
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<h2>What is the Surface Area of a Torus?</h2>
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<h2>What is the Surface Area of a Torus?</h2>
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<p>The surface area<a>of</a>a torus is the total area occupied by the boundary or surface of a torus. It is measured in<a>square</a>units.</p>
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<p>The surface area<a>of</a>a torus is the total area occupied by the boundary or surface of a torus. It is measured in<a>square</a>units.</p>
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<p>A torus is a 3D shape formed by revolving a circle around an axis that is coplanar with the circle.</p>
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<p>A torus is a 3D shape formed by revolving a circle around an axis that is coplanar with the circle.</p>
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<p>The torus has a ring shape with a hole in the middle, similar to a doughnut. It consists of a circular tube, and its surface area includes the entire outer boundary of this tube.</p>
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<p>The torus has a ring shape with a hole in the middle, similar to a doughnut. It consists of a circular tube, and its surface area includes the entire outer boundary of this tube.</p>
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<h2>Surface Area of a Torus Formula</h2>
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<h2>Surface Area of a Torus Formula</h2>
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<p>The surface area of a torus depends on the radii of the two circles involved: the radius of the tube (r) and the distance from the center of the tube to the center of the torus (R).</p>
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<p>The surface area of a torus depends on the radii of the two circles involved: the radius of the tube (r) and the distance from the center of the tube to the center of the torus (R).</p>
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<p>The<a>formula</a>for the surface area of a torus is given as: Surface Area = 4π²rR square units</p>
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<p>The<a>formula</a>for the surface area of a torus is given as: Surface Area = 4π²rR square units</p>
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<p>Here, r is the radius of the tube of the torus. R is the distance from the center of the tube to the center of the torus.</p>
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<p>Here, r is the radius of the tube of the torus. R is the distance from the center of the tube to the center of the torus.</p>
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<h2>Examples of Surface Area of a Torus</h2>
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<h2>Examples of Surface Area of a Torus</h2>
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<p>Let's consider examples involving different dimensions of a torus to calculate its surface area.</p>
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<p>Let's consider examples involving different dimensions of a torus to calculate its surface area.</p>
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<h2>Example 1: Surface Area of a Torus</h2>
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<h2>Example 1: Surface Area of a Torus</h2>
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<p>Find the surface area of a torus with a tube radius (r) of 3 cm and a distance (R) from the center of the tube to the center of the torus of 5 cm.</p>
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<p>Find the surface area of a torus with a tube radius (r) of 3 cm and a distance (R) from the center of the tube to the center of the torus of 5 cm.</p>
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<p>Using the formula: Surface Area = 4π²rR = 4 × 3.14² × 3 × 5 = 4 × 9.86 × 3 × 5 = 4 × 147.9 = 591.6 cm²</p>
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<p>Using the formula: Surface Area = 4π²rR = 4 × 3.14² × 3 × 5 = 4 × 9.86 × 3 × 5 = 4 × 147.9 = 591.6 cm²</p>
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<h2>Example 2: Surface Area of a Torus</h2>
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<h2>Example 2: Surface Area of a Torus</h2>
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<p>Calculate the surface area of a torus where the tube radius (r) is 2 cm and the distance (R) from the center of the tube to the center of the torus is 7 cm.</p>
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<p>Calculate the surface area of a torus where the tube radius (r) is 2 cm and the distance (R) from the center of the tube to the center of the torus is 7 cm.</p>
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<p>Surface Area = 4π²rR = 4 × 3.14² × 2 × 7 = 4 × 9.86 × 2 × 7 = 4 × 137.04 = 548.16 cm²</p>
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<p>Surface Area = 4π²rR = 4 × 3.14² × 2 × 7 = 4 × 9.86 × 2 × 7 = 4 × 137.04 = 548.16 cm²</p>
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<h2>Example 3: Surface Area of a Torus</h2>
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<h2>Example 3: Surface Area of a Torus</h2>
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<p>A torus has a tube radius (r) of 4 cm and a distance (R) from the center of the tube to the center of the torus of 10 cm. Find its surface area.</p>
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<p>A torus has a tube radius (r) of 4 cm and a distance (R) from the center of the tube to the center of the torus of 10 cm. Find its surface area.</p>
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<p>Surface Area = 4π²rR = 4 × 3.14² × 4 × 10 = 4 × 9.86 × 4 × 10 = 4 × 394.4 = 1577.6 cm²</p>
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<p>Surface Area = 4π²rR = 4 × 3.14² × 4 × 10 = 4 × 9.86 × 4 × 10 = 4 × 394.4 = 1577.6 cm²</p>
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<h2>Confusion between radii</h2>
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<h2>Confusion between radii</h2>
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<p>Students sometimes confuse the tube radius (r) with the distance (R) from the center of the tube to the center of the torus. Remember, r is the radius of the circular cross-section of the tube, and R is the larger radius from the center of the torus to the center of the tube.</p>
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<p>Students sometimes confuse the tube radius (r) with the distance (R) from the center of the tube to the center of the torus. Remember, r is the radius of the circular cross-section of the tube, and R is the larger radius from the center of the torus to the center of the tube.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 5 × 12 = 4 × 9.86 × 5 × 12 = 4 × 591.6 = 2366.4 cm²</p>
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<p>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 5 × 12 = 4 × 9.86 × 5 × 12 = 4 × 591.6 = 2366.4 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>Calculate the surface area of a torus where the tube radius is 6 cm and the distance from the center of the tube to the center of the torus is 8 cm.</p>
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<p>Calculate the surface area of a torus where the tube radius is 6 cm and the distance from the center of the tube to the center of the torus is 8 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 1184.64 cm²</p>
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<p>Surface Area = 1184.64 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: Surface Area = 4π²rR = 4 × 3.14² × 6 × 8 = 4 × 9.86 × 6 × 8 = 4 × 473.28 = 1893.12 cm²</p>
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<p>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 6 × 8 = 4 × 9.86 × 6 × 8 = 4 × 473.28 = 1893.12 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>Find the surface area of a torus with a tube radius of 7 cm and a distance from the center of the tube to the center of the torus of 9 cm.</p>
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<p>Find the surface area of a torus with a tube radius of 7 cm and a distance from the center of the tube to the center of the torus of 9 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 2484.36 cm²</p>
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<p>Surface Area = 2484.36 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>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 7 × 9 = 4 × 9.86 × 7 × 9 = 4 × 620.28 = 2481.12 cm²</p>
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<p>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 7 × 9 = 4 × 9.86 × 7 × 9 = 4 × 620.28 = 2481.12 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>A torus has a tube radius of 3 cm and a distance from the center of the tube to the center of the torus of 10 cm. What is its surface area?</p>
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<p>A torus has a tube radius of 3 cm and a distance from the center of the tube to the center of the torus of 10 cm. What is its surface area?</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 1183.2 cm²</p>
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<p>Surface Area = 1183.2 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>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 3 × 10 = 4 × 9.86 × 3 × 10 = 4 × 295.8 = 1183.2 cm²</p>
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<p>Use the formula: Surface Area = 4π²rR = 4 × 3.14² × 3 × 10 = 4 × 9.86 × 3 × 10 = 4 × 295.8 = 1183.2 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 surface area of a torus is 2000 cm², and the tube radius is 4 cm. Find the distance from the center of the tube to the center of the torus.</p>
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<p>The surface area of a torus is 2000 cm², and the tube radius is 4 cm. Find the distance from the center of the tube to the center of the torus.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Distance R = 10.12 cm</p>
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<p>Distance R = 10.12 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 outer surface of the torus, calculated using the formula 4π²rR.</h2>
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<h2>It is the total area that covers the outer surface of the torus, calculated using the formula 4π²rR.</h2>
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<h3>1.What are the two radii involved in the calculation of a torus's surface area?</h3>
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<h3>1.What are the two radii involved in the calculation of a torus's surface area?</h3>
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<p>The tube radius (r) and the distance (R) from the center of the tube to the center of the torus.</p>
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<p>The tube radius (r) and the distance (R) from the center of the tube to the center of the torus.</p>
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<h3>2.How is a torus formed?</h3>
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<h3>2.How is a torus formed?</h3>
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<p>A torus is formed by rotating a circle around an external axis coplanar with the circle.</p>
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<p>A torus is formed by rotating a circle around an external axis coplanar with the circle.</p>
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<h3>3.What unit is surface area measured in?</h3>
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<h3>3.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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<h3>4.Can a torus have different tube and central radii?</h3>
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<h3>4.Can a torus have different tube and central radii?</h3>
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<p>Yes, the tube radius (r) and the central radius (R) can vary, affecting the overall shape and surface area of the torus.</p>
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<p>Yes, the tube radius (r) and the central radius (R) can vary, affecting the overall shape and surface area of the torus.</p>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Torus</h2>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Torus</h2>
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<p>Students often make mistakes while calculating the surface area of a torus, leading to incorrect answers. Below are some common mistakes and how to avoid them.</p>
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<p>Students often make mistakes while calculating the surface area of a torus, leading to incorrect answers. Below are some common mistakes and how 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>