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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 of a cone is a 3-dimensional shape that results from slicing a cone parallel to its base. The surface area of the frustum of a cone is the total area covered by its outer surface. The surface area includes both its curved surface and its two circular bases. In this article, we will learn about the surface area of a frustum of a cone.</p>
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<p>A frustum of a cone is a 3-dimensional shape that results from slicing a cone parallel to its base. The surface area of the frustum of a cone is the total area covered by its outer surface. The surface area includes both its curved surface and its two circular bases. In this article, we will learn about the surface area of a frustum of a cone.</p>
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<h2>What is the Surface Area of the Frustum of a Cone?</h2>
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<h2>What is the Surface Area of the Frustum of a Cone?</h2>
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<p>The surface area<a>of</a>a frustum of a cone is the total area occupied by the boundary or surface of the frustum. It is measured in<a>square</a>units.</p>
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<p>The surface area<a>of</a>a frustum of a cone is the total area occupied by the boundary or surface of the frustum. It is measured in<a>square</a>units.</p>
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<p>A frustum is formed when a cone is sliced parallel to its<a>base</a>, resulting in a shape with two circular bases of different radii and a curved lateral surface.</p>
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<p>A frustum is formed when a cone is sliced parallel to its<a>base</a>, resulting in a shape with two circular bases of different radii and a curved lateral surface.</p>
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<p>The frustum has a top and bottom base, unlike the complete cone, and its surface area includes the curved surface area and the areas of both circular bases.</p>
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<p>The frustum has a top and bottom base, unlike the complete cone, and its surface area includes the curved surface area and the areas of both circular bases.</p>
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<h2>Surface Area of a Frustum of a Cone Formula</h2>
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<h2>Surface Area of a Frustum of a Cone Formula</h2>
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<p>A frustum of a cone has a curved surface and two circular bases, and its surface area is classified into the curved surface area and the total surface area.</p>
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<p>A frustum of a cone has a curved surface and two circular bases, and its surface area is classified into the curved surface area and the total surface area.</p>
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<p>Observe the frustum below to see its surface area, height (h), slant height (l), and the radii of the top (R) and bottom (r) bases.</p>
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<p>Observe the frustum below to see its surface area, height (h), slant height (l), and the radii of the top (R) and bottom (r) bases.</p>
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<p>A frustum has the following surface areas: Curved Surface Area of a Frustum Total Surface Area of a Frustum</p>
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<p>A frustum has the following surface areas: Curved Surface Area of a Frustum Total Surface Area of a Frustum</p>
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<h2>Curved Surface Area of a Frustum</h2>
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<h2>Curved Surface Area of a Frustum</h2>
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<p>The area of the curved part of the frustum, excluding its bases, is known as the curved surface area of a frustum.</p>
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<p>The area of the curved part of the frustum, excluding its bases, is known as the curved surface area of a frustum.</p>
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<p>The<a>formula</a>for the CSA (Curved Surface Area) of the frustum is given as: Curved Surface Area = π(R + r)l square units</p>
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<p>The<a>formula</a>for the CSA (Curved Surface Area) of the frustum is given as: Curved Surface Area = π(R + r)l square units</p>
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<p>Here, R is the radius of the top base of the frustum, r is the radius of the bottom base of the frustum, and l is the slant height of the frustum.</p>
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<p>Here, R is the radius of the top base of the frustum, r is the radius of the bottom base of the frustum, 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 area occupied by the frustum, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of the frustum.</p>
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<p>The total area occupied by the frustum, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of the frustum.</p>
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<p>The total surface area is calculated using the formula: Total Surface Area = π(R + r)l + πR² + πr² square units</p>
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<p>The total surface area is calculated using the formula: Total Surface Area = π(R + r)l + πR² + πr² square units</p>
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<p>Where R is the radius of the top base, r is the radius of the bottom base, and l is the slant height of the frustum.</p>
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<p>Where R is the radius of the top base, r is the radius of the bottom base, and l is the slant height of the frustum.</p>
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<p>Derivation of the Total Surface Area of a Frustum</p>
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<p>Derivation of the Total Surface Area of a Frustum</p>
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<p>To find the total surface area of a frustum, consider its<a>geometry</a>, which includes the two circular bases and the curved surface.</p>
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<p>To find the total surface area of a frustum, consider its<a>geometry</a>, which includes the two circular bases and the curved surface.</p>
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<p>Total surface area of a frustum = base area of the top circle + base area of the bottom circle + curved surface area of the frustum</p>
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<p>Total surface area of a frustum = base area of the top circle + base area of the bottom circle + curved surface area of the frustum</p>
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<p>Here, base area of top circle = πR²</p>
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<p>Here, base area of top circle = πR²</p>
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<p>base area of bottom circle = πr²</p>
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<p>base area of bottom circle = πr²</p>
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<p>Curved surface area of a frustum = π(R + r)l</p>
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<p>Curved surface area of a frustum = π(R + r)l</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 of a frustum, T = πR² + πr² + π(R + r)l</p>
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<p>Total surface area of a frustum, T = πR² + πr² + π(R + r)l</p>
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<p>Therefore, the total surface area of the frustum T = π(R² + r² + (R + r)l)</p>
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<p>Therefore, the total surface area of the frustum T = π(R² + r² + (R + r)l)</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 shows how much space is inside it. It tells us how much space the frustum can hold. The volume of a frustum can be found using the formula: Volume = (1/3)πh(R² + r² + Rr) (cubic units) Where h is the height of the frustum, R is the radius of the top base, and r is the radius of the bottom base.</p>
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<p>The volume of a frustum shows how much space is inside it. It tells us how much space the frustum can hold. The volume of a frustum can be found using the formula: Volume = (1/3)πh(R² + r² + Rr) (cubic units) Where h is the height of the frustum, R is the radius of the top base, and r is the radius of the bottom base.</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 frustum are the same. This confusion arises because both involve the slant height and the radii of the bases. Always remember that CSA involves only the curved side of the frustum, 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 frustum are the same. This confusion arises because both involve the slant height and the radii of the bases. Always remember that CSA involves only the curved side of the frustum, 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 = 5 cm, r = 8 cm, l = 10 cm. Use the formula: CSA = π(R + r)l = (22/7) × (5 + 8) × 10 = (22/7) × 13 × 10 = 22 × 130/7 = 408 cm²</p>
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<p>Given R = 5 cm, r = 8 cm, l = 10 cm. Use the formula: CSA = π(R + r)l = (22/7) × (5 + 8) × 10 = (22/7) × 13 × 10 = 22 × 130/7 = 408 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 top radius 4 cm, bottom radius 7 cm, and slant height 12 cm.</p>
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<p>Find the total surface area of a frustum with top radius 4 cm, bottom radius 7 cm, and slant height 12 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>TSA = 692.2 cm²</p>
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<p>TSA = 692.2 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 = π(R² + r² + (R + r)l) = 3.14 × (4² + 7² + (4 + 7) × 12) = 3.14 × (16 + 49 + 11 × 12) = 3.14 × (65 + 132) = 3.14 × 197 = 692.2 cm²</p>
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<p>Use the formula: TSA = π(R² + r² + (R + r)l) = 3.14 × (4² + 7² + (4 + 7) × 12) = 3.14 × (16 + 49 + 11 × 12) = 3.14 × (65 + 132) = 3.14 × 197 = 692.2 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 frustum has a top radius of 6 cm, bottom radius of 10 cm, and a height of 15 cm. Find the total surface area.</p>
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<p>A frustum has a top radius of 6 cm, bottom radius of 10 cm, and a height of 15 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 = 1222.56 cm²</p>
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<p>TSA = 1222.56 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>Find the slant height using: l = √((10 - 6)² + 15²) = √(16 + 225) = √241 = 15.52 cm Use the TSA formula: TSA = π(R² + r² + (R + r)l) = 3.14 × (6² + 10² + (6 + 10) × 15.52) = 3.14 × (36 + 100 + 248.32) = 3.14 × 384.32 = 1222.56 cm²</p>
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<p>Find the slant height using: l = √((10 - 6)² + 15²) = √(16 + 225) = √241 = 15.52 cm Use the TSA formula: TSA = π(R² + r² + (R + r)l) = 3.14 × (6² + 10² + (6 + 10) × 15.52) = 3.14 × (36 + 100 + 248.32) = 3.14 × 384.32 = 1222.56 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 frustum with top radius 3 cm, bottom radius 6 cm, and slant height 8 cm.</p>
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<p>Find the curved surface area of a frustum with top radius 3 cm, bottom 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>CSA = 226.08 cm²</p>
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<p>CSA = 226.08 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 = π(R + r)l = (22/7) × (3 + 6) × 8 = (22/7) × 9 × 8 = 22 × 72/7 = 226.08 cm²</p>
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<p>CSA = π(R + r)l = (22/7) × (3 + 6) × 8 = (22/7) × 9 × 8 = 22 × 72/7 = 226.08 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>The slant height of a frustum is 9 cm, and its curved surface area is 396 cm². The top radius is 7 cm. Find the bottom radius.</p>
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<p>The slant height of a frustum is 9 cm, and its curved surface area is 396 cm². The top radius is 7 cm. Find the bottom radius.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Bottom Radius = 9 cm</p>
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<p>Bottom Radius = 9 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 frustum, including its curved side and the areas of both circular bases.</h2>
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<h2>It is the total area that covers the outer surface of the frustum, including its curved side and the areas of both circular bases.</h2>
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<h3>1.What are the two types of surface area in a frustum?</h3>
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<h3>1.What are the two types of surface area in a frustum?</h3>
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<p>Curved surface area and total surface area are the two types of surface area in a frustum.</p>
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<p>Curved surface area and total surface area are the two types of surface area in a frustum.</p>
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<h3>2.What is the difference between slant height and height?</h3>
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<h3>2.What is the difference between slant height and height?</h3>
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<p>Slant height is the length from the top edge of the frustum to the bottom edge. Height is the vertical distance between the two bases.</p>
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<p>Slant height is the length from the top edge of the frustum to the bottom edge. Height is the vertical distance between the two bases.</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 frustums, both curved and lateral surface area mean the same.</p>
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<p>Yes, in frustums, 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 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>