Mensuration

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A right circular cylinder is a solid formed when a rectangle is revolved about one of its sides as an axis. The side about which the rectangle revolves becomes the height of the cylinder, and the oppo

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Curved Surface Area of Cylinder = 2πrh Where: r = radius of base, h = height Alternatively: Curved Surface Area = Perimeter of base × Height

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Total Surface Area of Cylinder = 2πr(h + r) This includes: Curved surface area + Area of top + Area of bottom = 2πrh + πr² + πr² = 2πrh + 2πr²

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Volume of Cylinder = πr²h Where: r = radius of base, h = height Concept: Volume = Area of base × Height

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Given: r = 3.5 m, h = 10 m Total Surface Area = 2πr(h + r) = 2 × (22/7) × 3.5 × (10 + 3.5) = 2 × (22/7) × 3.5 × 13.5 = 297 m²

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A hollow cylinder is a cylinder with a hollow interior (like pipes or tubes). Volume of material = π(R² - r²)h Where: R = external radius, r = internal radius, h = height This equals: External volume

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A right circular cone is formed by revolving a right-angled triangle about one of its sides containing the right angle. Important parts: - Vertex: The top point - Base: Circular bottom (radius = r) -

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l² = h² + r² Or: l = √(h² + r²) Where: l = slant height, h = height, r = radius of base This comes from Pythagoras theorem applied to the right triangle formed.