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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 hemisphere is a three-dimensional shape that represents half of a sphere. The surface area of a hemisphere includes both the curved surface and the circular base. In this article, we will learn about the surface area of a hemisphere.</p>
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<p>A hemisphere is a three-dimensional shape that represents half of a sphere. The surface area of a hemisphere includes both the curved surface and the circular base. In this article, we will learn about the surface area of a hemisphere.</p>
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<h2>What is the Surface Area of a Hemisphere?</h2>
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<h2>What is the Surface Area of a Hemisphere?</h2>
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<p>The surface area of a hemisphere is the total area occupied by the boundary or surface of a hemisphere. It is measured in<a>square</a>units.</p>
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<p>The surface area of a hemisphere is the total area occupied by the boundary or surface of a hemisphere. It is measured in<a>square</a>units.</p>
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<p>A hemisphere has a curved surface and a flat circular<a>base</a>, so it has two surface areas: the curved surface area and the total surface area. A hemisphere is essentially half of a sphere, split along its diameter.</p>
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<p>A hemisphere has a curved surface and a flat circular<a>base</a>, so it has two surface areas: the curved surface area and the total surface area. A hemisphere is essentially half of a sphere, split along its diameter.</p>
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<h2>Surface Area of a Hemisphere Formula</h2>
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<h2>Surface Area of a Hemisphere Formula</h2>
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<p>A hemisphere has a curved surface, which contributes to two types of surface areas: the curved surface area and the total surface area. Look at the hemisphere below to understand its surface area and radius (r).</p>
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<p>A hemisphere has a curved surface, which contributes to two types of surface areas: the curved surface area and the total surface area. Look at the hemisphere below to understand its surface area and radius (r).</p>
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<p>A hemisphere has two types of surface areas:</p>
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<p>A hemisphere has two types of surface areas:</p>
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<ol><li>Curved Surface Area of a Hemisphere</li>
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<ol><li>Curved Surface Area of a Hemisphere</li>
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<li>Total Surface Area of a Hemisphere</li>
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<li>Total Surface Area of a Hemisphere</li>
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</ol><h2>Curved Surface Area of a Hemisphere</h2>
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</ol><h2>Curved Surface Area of a Hemisphere</h2>
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<p>The area of the curved part of the hemisphere, excluding its base, is known as the curved surface area of a hemisphere.</p>
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<p>The area of the curved part of the hemisphere, excluding its base, is known as the curved surface area of a hemisphere.</p>
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<p>The<a>formula</a>for the CSA (Curved Surface Area) of the hemisphere is given as:</p>
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<p>The<a>formula</a>for the CSA (Curved Surface Area) of the hemisphere is given as:</p>
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<p>Curved Surface Area = 2πr² square units</p>
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<p>Curved Surface Area = 2πr² square units</p>
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<p>Here, r is the radius of the base of a hemisphere.</p>
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<p>Here, r is the radius of the base of a hemisphere.</p>
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<h2>Total Surface Area of a Hemisphere</h2>
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<h2>Total Surface Area of a Hemisphere</h2>
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<p>The total area occupied by the hemisphere, including the area of the curved surface and the area of the circular base, is known as the total surface area of the hemisphere.</p>
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<p>The total area occupied by the hemisphere, including the area of the curved surface and the area of the circular base, is known as the total surface area of the hemisphere.</p>
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<p>The formula is: Total Surface Area = 3πr² square units</p>
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<p>The formula is: Total Surface Area = 3πr² square units</p>
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<p>Where r is the radius of the base of the hemisphere.</p>
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<p>Where r is the radius of the base of the hemisphere.</p>
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<p>Derivation of the Total Surface Area of a Hemisphere:</p>
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<p>Derivation of the Total Surface Area of a Hemisphere:</p>
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<p>To find the total surface area of a hemisphere, consider both its curved surface and the base.</p>
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<p>To find the total surface area of a hemisphere, consider both its curved surface and the base.</p>
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<p>The base area of a hemisphere = πr².</p>
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<p>The base area of a hemisphere = πr².</p>
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<p>Curved surface area of a hemisphere = 2πr².</p>
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<p>Curved surface area of a hemisphere = 2πr².</p>
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<p>By adding these, Total surface area = base area + curved surface area = πr² + 2πr² = 3πr²</p>
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<p>By adding these, Total surface area = base area + curved surface area = πr² + 2πr² = 3πr²</p>
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<h2>Volume of a Hemisphere</h2>
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<h2>Volume of a Hemisphere</h2>
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<p>The volume of a hemisphere shows how much space it contains. It is half of the volume of a sphere with the same radius.</p>
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<p>The volume of a hemisphere shows how much space it contains. It is half of the volume of a sphere with the same radius.</p>
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<p>The volume can be calculated using the formula: Volume = (2/3)πr³ cubic units</p>
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<p>The volume can be calculated using the formula: Volume = (2/3)πr³ cubic units</p>
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<h2>Confusion between CSA and TSA</h2>
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<h2>Confusion between CSA and TSA</h2>
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<p>Students sometimes confuse the curved surface area (CSA) and total surface area (TSA) of a hemisphere. Remember, CSA includes only the curved surface, while TSA includes both the curved surface and the base.</p>
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<p>Students sometimes confuse the curved surface area (CSA) and total surface area (TSA) of a hemisphere. Remember, CSA includes only the curved surface, while TSA includes both the curved surface and the base.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Given r = 7 cm. Use the formula: CSA = 2πr² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 cm²</p>
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<p>Given r = 7 cm. Use the formula: CSA = 2πr² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 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 hemisphere with a radius of 5 cm.</p>
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<p>Find the total surface area of a hemisphere with a radius of 5 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>TSA = 235.5 cm²</p>
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<p>TSA = 235.5 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: TSA = 3πr² = 3 × 3.14 × 5² = 3 × 3.14 × 25 = 3 × 78.5 = 235.5 cm²</p>
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<p>Use the formula: TSA = 3πr² = 3 × 3.14 × 5² = 3 × 3.14 × 25 = 3 × 78.5 = 235.5 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 hemisphere has a radius of 6 cm. Find the total surface area.</p>
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<p>A hemisphere has a radius of 6 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>TSA = 339.12 cm²</p>
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<p>TSA = 339.12 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Use the TSA formula: TSA = 3πr² = 3 × 3.14 × 6² = 3 × 3.14 × 36 = 3 × 113.04 = 339.12 cm²</p>
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<p>Use the TSA formula: TSA = 3πr² = 3 × 3.14 × 6² = 3 × 3.14 × 36 = 3 × 113.04 = 339.12 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 curved surface area of a hemisphere with a radius of 3.5 cm.</p>
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<p>Find the curved surface area of a hemisphere with a radius of 3.5 cm.</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>CSA = 2πr² = 2 × (22/7) × 3.5 × 3.5 = 2 × 22 × 0.5 × 3.5 = 2 × 11 × 3.5 = 77 cm²</p>
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<p>CSA = 2πr² = 2 × (22/7) × 3.5 × 3.5 = 2 × 22 × 0.5 × 3.5 = 2 × 11 × 3.5 = 77 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 curved surface area of a hemisphere is 660 cm². Find the radius.</p>
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<p>The curved surface area of a hemisphere is 660 cm². Find the radius.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Radius = 10 cm</p>
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<p>Radius = 10 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 hemisphere, including its curved surface and the base.</h2>
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<h2>It is the total area that covers the outside of the hemisphere, including its curved surface and the base.</h2>
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<h3>1.What are the two types of surface area in a hemisphere?</h3>
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<h3>1.What are the two types of surface area in a hemisphere?</h3>
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<p>Curved surface area and total surface area are the two types of surface area in a hemisphere.</p>
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<p>Curved surface area and total surface area are the two types of surface area in a hemisphere.</p>
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<h3>2.How does the curved surface area differ from the total surface area?</h3>
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<h3>2.How does the curved surface area differ from the total surface area?</h3>
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<p>The curved surface area covers only the curved part of the hemisphere, while the total surface area includes both the curved surface and the base.</p>
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<p>The curved surface area covers only the curved part of the hemisphere, while the total surface area includes both the curved surface and the base.</p>
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<h3>3.Is curved surface area the same as lateral surface area?</h3>
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<h3>3.Is curved surface area the same as lateral surface area?</h3>
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<p>Yes, in hemispheres, both curved and lateral surface area mean the same.</p>
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<p>Yes, in hemispheres, both curved and lateral surface area mean the same.</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 Hemisphere</h2>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Hemisphere</h2>
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<p>Students often make mistakes while calculating the surface area of a hemisphere, leading to incorrect answers. Below are some common mistakes and ways to avoid them.</p>
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<p>Students often make mistakes while calculating the surface area of a hemisphere, leading to incorrect answers. Below are some common mistakes and 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>