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<p>Last updated on<strong>August 30, 2025</strong></p>
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<p>Last updated on<strong>August 30, 2025</strong></p>
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<p>A closed cylinder is a 3-dimensional shape with two parallel circular bases and a curved surface connecting them. The surface area of a closed cylinder is the total area covered by its outer surface, including both its curved surface and its two circular bases. In this article, we will learn about the surface area of a closed cylinder.</p>
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<p>A closed cylinder is a 3-dimensional shape with two parallel circular bases and a curved surface connecting them. The surface area of a closed cylinder is the total area covered by its outer surface, including both its curved surface and its two circular bases. In this article, we will learn about the surface area of a closed cylinder.</p>
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<h2>What is the Surface Area of a Closed Cylinder?</h2>
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<h2>What is the Surface Area of a Closed Cylinder?</h2>
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<p>The surface area<a>of</a>a closed cylinder is the total area occupied by the boundary or surface of the cylinder. It is measured in<a>square</a>units.</p>
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<p>The surface area<a>of</a>a closed cylinder is the total area occupied by the boundary or surface of the cylinder. It is measured in<a>square</a>units.</p>
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<p>A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.</p>
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<p>A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.</p>
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<p>The surface area of a closed cylinder includes the area of the curved surface and the areas of the two circular bases.</p>
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<p>The surface area of a closed cylinder includes the area of the curved surface and the areas of the two circular bases.</p>
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<p>Cylinders are classified into right circular cylinders and oblique cylinders.</p>
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<p>Cylinders are classified into right circular cylinders and oblique cylinders.</p>
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<p>A right circular cylinder has its axis perpendicular to its bases, while an oblique cylinder has its axis tilted.</p>
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<p>A right circular cylinder has its axis perpendicular to its bases, while an oblique cylinder has its axis tilted.</p>
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<h2>Surface Area of a Closed Cylinder Formula</h2>
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<h2>Surface Area of a Closed Cylinder Formula</h2>
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<p>A closed cylinder has both a curved surface area and two<a>base</a>areas.</p>
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<p>A closed cylinder has both a curved surface area and two<a>base</a>areas.</p>
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<p>Look at the cylinder below to see its surface area, height (h), and radius (r).</p>
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<p>Look at the cylinder below to see its surface area, height (h), and radius (r).</p>
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<p>A closed cylinder has:</p>
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<p>A closed cylinder has:</p>
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<p>Curved Surface Area of a Cylinder</p>
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<p>Curved Surface Area of a Cylinder</p>
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<p>Total Surface Area of a Closed Cylinder</p>
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<p>Total Surface Area of a Closed Cylinder</p>
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<h2>Curved Surface Area of a Cylinder</h2>
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<h2>Curved Surface Area of a Cylinder</h2>
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<p>The area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.</p>
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<p>The area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.</p>
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<p>The curved surface area (CSA) of a cylinder is given by the<a>formula</a>:</p>
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<p>The curved surface area (CSA) of a cylinder is given by the<a>formula</a>:</p>
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<p>Curved Surface Area = 2πrh square units</p>
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<p>Curved Surface Area = 2πrh square units</p>
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<p>Here, r is the radius of the base of the cylinder. h is the height of the cylinder.</p>
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<p>Here, r is the radius of the base of the cylinder. h is the height of the cylinder.</p>
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<h2>Total Surface Area of a Closed Cylinder</h2>
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<h2>Total Surface Area of a Closed Cylinder</h2>
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<p>The total area occupied by the cylinder, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of a closed cylinder.</p>
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<p>The total area occupied by the cylinder, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of a closed cylinder.</p>
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<p>The total surface area (TSA) is calculated using the formula:</p>
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<p>The total surface area (TSA) is calculated using the formula:</p>
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<p>Total surface area = 2πr(r + h) square units Where r is the radius of the base of the cylinder. h is the height of the cylinder.</p>
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<p>Total surface area = 2πr(r + h) square units Where r is the radius of the base of the cylinder. h is the height of the cylinder.</p>
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<p>Derivation of the Total Surface Area of a Closed Cylinder To find the total surface area of a closed cylinder, consider the curved surface and the two circular bases.</p>
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<p>Derivation of the Total Surface Area of a Closed Cylinder To find the total surface area of a closed cylinder, consider the curved surface and the two circular bases.</p>
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<p>Total surface area of a closed cylinder = base area + curved surface area + base area</p>
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<p>Total surface area of a closed cylinder = base area + curved surface area + base area</p>
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<p>Here, the base area of the cylinder = πr²</p>
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<p>Here, the base area of the cylinder = πr²</p>
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<p>Curved surface area of the cylinder = 2πrh</p>
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<p>Curved surface area of the cylinder = 2πrh</p>
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<p>Substituting the formulas into the total surface area,</p>
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<p>Substituting the formulas into the total surface area,</p>
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<p>Total surface area = 2πr² + 2πrh</p>
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<p>Total surface area = 2πr² + 2πrh</p>
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<p>Take the common<a>terms</a>out: TSA = 2πr(r + h)</p>
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<p>Take the common<a>terms</a>out: TSA = 2πr(r + h)</p>
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<h2>Volume of a Cylinder</h2>
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<h2>Volume of a Cylinder</h2>
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<p>The volume of a cylinder shows how much space is inside it. It is the<a>product</a>of the area of the base and the height.</p>
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<p>The volume of a cylinder shows how much space is inside it. It is the<a>product</a>of the area of the base and the height.</p>
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<p>The volume of a cylinder can be found by using the formula: Volume = πr²h (cubic units)</p>
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<p>The volume of a cylinder can be found by using the formula: Volume = πr²h (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 assume that the curved surface area (CSA) and the total surface area (TSA) of a closed cylinder are the same. This confusion arises because both involve the height and the radius. Always remember that CSA is only for the curved side, while TSA includes the curved surface and both bases.</p>
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<p>Students assume that the curved surface area (CSA) and the total surface area (TSA) of a closed cylinder are the same. This confusion arises because both involve the height and the radius. Always remember that CSA is only for the curved side, while TSA includes the curved surface and both 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 = 7 cm, h = 10 cm. Use the formula: CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm²</p>
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<p>Given r = 7 cm, h = 10 cm. Use the formula: CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 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 cylinder with a radius of 5 cm and a height of 13 cm.</p>
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<p>Find the total surface area of a cylinder with a radius of 5 cm and a height of 13 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>TSA = 565.2 cm²</p>
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<p>TSA = 565.2 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 13) = 2 × 3.14 × 5 × 18 = 565.2 cm²</p>
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<p>Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 13) = 2 × 3.14 × 5 × 18 = 565.2 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>A cylinder has a radius of 6 cm and a height of 8 cm. Find the total surface area.</p>
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<p>A cylinder has a radius of 6 cm and a height of 8 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 = 528 cm²</p>
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<p>TSA = 528 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 = 2πr(r + h) = 2 × 3.14 × 6 × (6 + 8) = 2 × 3.14 × 6 × 14 = 528 cm²</p>
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<p>Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 6 × (6 + 8) = 2 × 3.14 × 6 × 14 = 528 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 cylinder with a radius of 3.5 cm and a height of 5 cm.</p>
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<p>Find the curved surface area of a cylinder with a radius of 3.5 cm and a height of 5 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>CSA = 110 cm²</p>
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<p>CSA = 110 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 = 2πrh = 2 × (22/7) × 3.5 × 5 = 110 cm²</p>
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<p>CSA = 2πrh = 2 × (22/7) × 3.5 × 5 = 110 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 height of a cylinder is 15 cm, and its curved surface area is 660 cm². Find the radius.</p>
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<p>The height of a cylinder is 15 cm, and its curved surface area 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 = 7 cm</p>
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<p>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 cylinder, including its curved surface and the two circular bases.</h2>
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<h2>It is the total area that covers the outside of the cylinder, including its curved surface and the two circular bases.</h2>
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<h3>1.What are the two types of surface area in a cylinder?</h3>
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<h3>1.What are the two types of surface area in a cylinder?</h3>
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<p>Curved surface area and total surface area are the two types of surface area in a cylinder.</p>
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<p>Curved surface area and total surface area are the two types of surface area in a cylinder.</p>
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<h3>2.What is the difference between diameter and radius?</h3>
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<h3>2.What is the difference between diameter and radius?</h3>
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<p>The radius is the distance from the center of the base to its edge, while the diameter is twice the radius.</p>
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<p>The radius is the distance from the center of the base to its edge, while the diameter is twice the radius.</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 cylinders, both curved and lateral surface area mean the same.</p>
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<p>Yes, in cylinders, 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 Closed Cylinder</h2>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Closed Cylinder</h2>
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<p>Students often make mistakes while calculating the surface area of a closed cylinder, which leads 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 closed cylinder, which leads 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>