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2026-01-01
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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 solid is a three-dimensional object that occupies space and has a surface. The surface area of a solid is the total area covered by all its outer surfaces. This includes any flat, curved, or irregular surfaces that make up the solid. In this article, we will explore the concept of surface area for various solids.</p>
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<p>A solid is a three-dimensional object that occupies space and has a surface. The surface area of a solid is the total area covered by all its outer surfaces. This includes any flat, curved, or irregular surfaces that make up the solid. In this article, we will explore the concept of surface area for various solids.</p>
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<h2>What is the Surface Area of a Solid?</h2>
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<h2>What is the Surface Area of a Solid?</h2>
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<p>The surface area of a solid is the total area occupied by the boundary or surface of the solid. It is measured in<a>square</a>units.</p>
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<p>The surface area of a solid is the total area occupied by the boundary or surface of the solid. It is measured in<a>square</a>units.</p>
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<p>Solids can have flat surfaces, such as the faces of a<a>cube</a>, or curved surfaces, such as those of a sphere. Understanding the surface area of a solid involves calculating the area of all its external surfaces.</p>
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<p>Solids can have flat surfaces, such as the faces of a<a>cube</a>, or curved surfaces, such as those of a sphere. Understanding the surface area of a solid involves calculating the area of all its external surfaces.</p>
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<p>Different types of solids include prisms, cylinders, cones, and spheres, each with unique surface area<a>formulas</a>.</p>
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<p>Different types of solids include prisms, cylinders, cones, and spheres, each with unique surface area<a>formulas</a>.</p>
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<h2>Surface Area of a Solid Formula</h2>
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<h2>Surface Area of a Solid Formula</h2>
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<p>Different solids have different formulas to calculate their surface areas. These formulas depend on the shape and dimensions of the solid.</p>
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<p>Different solids have different formulas to calculate their surface areas. These formulas depend on the shape and dimensions of the solid.</p>
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<p>Below are some common solids and their surface area considerations:</p>
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<p>Below are some common solids and their surface area considerations:</p>
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<p>Solids with flat surfaces: Calculate the area of each face and<a>sum</a>them up.</p>
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<p>Solids with flat surfaces: Calculate the area of each face and<a>sum</a>them up.</p>
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<p>Solids with curved surfaces: Use specific formulas for the curved parts.</p>
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<p>Solids with curved surfaces: Use specific formulas for the curved parts.</p>
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<p>Combined solids: Consider both flat and curved areas in the calculation.</p>
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<p>Combined solids: Consider both flat and curved areas in the calculation.</p>
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<h2>Surface Area of a Cylinder</h2>
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<h2>Surface Area of a Cylinder</h2>
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<p>A cylinder has two flat circular bases and a curved surface connecting them. The curved surface area is known as the lateral surface area, and the total surface area includes both the curved surface and the two bases.</p>
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<p>A cylinder has two flat circular bases and a curved surface connecting them. The curved surface area is known as the lateral surface area, and the total surface area includes both the curved surface and the two bases.</p>
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<p>The formulas are: Curved Surface Area of a Cylinder = 2πrh square units</p>
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<p>The formulas are: Curved Surface Area of a Cylinder = 2πrh square units</p>
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<p>Total Surface Area of a Cylinder = 2πr(r + h) square units</p>
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<p>Total Surface Area of a Cylinder = 2πr(r + h) square units</p>
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<p>where r is the radius of the<a>base</a>, h is the height of the cylinder.</p>
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<p>where r is the radius of the<a>base</a>, h is the height of the cylinder.</p>
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<h2>Surface Area of a Sphere</h2>
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<h2>Surface Area of a Sphere</h2>
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<p>A sphere is a perfectly round solid with a single curved surface and no edges or vertices.</p>
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<p>A sphere is a perfectly round solid with a single curved surface and no edges or vertices.</p>
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<p>The surface area of a sphere is calculated using the formula: Surface Area of a Sphere = 4πr² square units</p>
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<p>The surface area of a sphere is calculated using the formula: Surface Area of a Sphere = 4πr² square units</p>
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<p>where r is the radius of the sphere.</p>
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<p>where r is the radius of the sphere.</p>
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<h2>Surface Area of a Prism</h2>
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<h2>Surface Area of a Prism</h2>
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<p>A prism has two parallel bases and rectangular lateral faces.</p>
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<p>A prism has two parallel bases and rectangular lateral faces.</p>
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<p>The total surface area is the sum of the areas of all its faces.</p>
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<p>The total surface area is the sum of the areas of all its faces.</p>
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<p>For a rectangular prism, the formula is: Total Surface Area = 2lw + 2lh + 2wh square units where l is the length, w is the width, and h is the height.</p>
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<p>For a rectangular prism, the formula is: Total Surface Area = 2lw + 2lh + 2wh square units where l is the length, w is the width, and h is the height.</p>
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<h2>Confusion between Lateral and Total Surface Area</h2>
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<h2>Confusion between Lateral and Total Surface Area</h2>
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<p>Students often confuse lateral surface area with total surface area. Lateral surface area refers only to the sides of a solid, excluding the bases, while total surface area includes all surfaces. Ensure clarity of which area needs calculation.</p>
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<p>Students often confuse lateral surface area with total surface area. Lateral surface area refers only to the sides of a solid, excluding the bases, while total surface area includes all surfaces. Ensure clarity of which area needs calculation.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 5 × 12 = 377 cm²</p>
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<p>Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 5 × 12 = 377 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 sphere with a radius of 7 cm.</p>
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<p>Find the total surface area of a sphere with a radius of 7 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>TSA = 615.44 cm²</p>
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<p>TSA = 615.44 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 = 4πr² = 4 × 3.14 × 7² = 4 × 3.14 × 49 = 615.44 cm²</p>
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<p>Use the formula: TSA = 4πr² = 4 × 3.14 × 7² = 4 × 3.14 × 49 = 615.44 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 rectangular prism has dimensions of length 8 cm, width 4 cm, and height 3 cm. Find the total surface area.</p>
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<p>A rectangular prism has dimensions of length 8 cm, width 4 cm, and height 3 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 = 136 cm²</p>
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<p>TSA = 136 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: TSA = 2lw + 2lh + 2wh = 2(8 × 4) + 2(8 × 3) + 2(4 × 3) = 64 + 48 + 24 = 136 cm²</p>
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<p>Use the formula: TSA = 2lw + 2lh + 2wh = 2(8 × 4) + 2(8 × 3) + 2(4 × 3) = 64 + 48 + 24 = 136 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 cone with a radius of 3 cm and a slant height of 8 cm.</p>
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<p>Find the surface area of a cone with a radius of 3 cm and a slant height of 8 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>CSA = 75.36 cm²</p>
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<p>CSA = 75.36 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>CSA = πrl = 3.14 × 3 × 8 = 75.36 cm²</p>
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<p>CSA = πrl = 3.14 × 3 × 8 = 75.36 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 total surface area of a cylinder is 282.6 cm² with a height of 6 cm. Find the radius.</p>
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<p>The total surface area of a cylinder is 282.6 cm² with a height of 6 cm. Find the radius.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Radius = 3 cm</p>
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<p>Radius = 3 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 external surfaces of a solid, including any flat, curved, or irregular surfaces.</h2>
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<h2>It is the total area that covers the external surfaces of a solid, including any flat, curved, or irregular surfaces.</h2>
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<h3>1.What are the types of surface area calculations in solids?</h3>
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<h3>1.What are the types of surface area calculations in solids?</h3>
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<p>Typically, we calculate lateral surface area and total surface area, depending on whether bases are included.</p>
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<p>Typically, we calculate lateral surface area and total surface area, depending on whether bases are included.</p>
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<h3>2.How does slant height differ from height?</h3>
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<h3>2.How does slant height differ from height?</h3>
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<p>Slant height applies to solids with curved surfaces, like cones, and is the diagonal distance from the top to the base edge. Height is the vertical distance from top to base center.</p>
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<p>Slant height applies to solids with curved surfaces, like cones, and is the diagonal distance from the top to the base edge. Height is the vertical distance from top to base center.</p>
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<h3>3.Is curved surface area always different from lateral surface area?</h3>
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<h3>3.Is curved surface area always different from lateral surface area?</h3>
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<p>In some solids, like cones and cylinders, curved surface area and lateral surface area are the same.</p>
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<p>In some solids, like cones and cylinders, curved surface area and lateral surface area are 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 Calculating Surface Area of Solids</h2>
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<h2>Common Mistakes and How to Avoid Them in Calculating Surface Area of Solids</h2>
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<p>Students often make mistakes while calculating the surface area of various solids, which leads to incorrect results. 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 various solids, which leads to incorrect results. 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>