Mensuration

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Curved Surface Area (CSA) is the area of only the curved surfaces of a solid, excluding flat surfaces like bases. Total Surface Area (TSA) is the area of all surfaces including curved surfaces and fla

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Curved Surface Area of cylinder = 2πrh, where r is the radius of the base and h is the height of the cylinder.

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Total Surface Area of sphere = 4πr², where r is the radius of the sphere. Note: For a sphere, curved surface area and total surface area are the same since it has no flat surfaces.

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Given: r = 7m, h = 10m Slant height (l) = √(r² + h²) = √(49 + 100) = √149 = 12.2m Curved Surface Area = πrl = (22/7) × 7 × 12.2 = 268.4 m²

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Volume of hemisphere = (2/3)πr³, where r is the radius. This is exactly half the volume of a complete sphere (4/3)πr³.

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When solids are combined, some surfaces get hidden or coincide at the joining points. These hidden surfaces are not part of the external surface area of the combined solid. For example, when a cone is

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When a solid is converted from one shape to another (like melting and recasting), the volume always remains the same. This principle is used to solve problems involving conversion of solids. Volume of

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Total Surface Area of cuboid = 2(lb + bh + hl), where l is length, b is breadth, and h is height.