Surface Areas and Volumes

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A right circular cone is a solid figure formed by rotating a right-angled triangle about one of its perpendicular sides. Key components: Vertex (top point), Height (h) - perpendicular distance from ve…

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By Pythagoras theorem: l² = r² + h², therefore l = √(r² + h²). The slant height is the hypotenuse of the right triangle formed by height and radius.

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Curved Surface Area of a Cone = πrl, where r is the base radius and l is the slant height. This formula comes from unfolding the cone into a sector of a circle.

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Total Surface Area of a Cone = πrl + πr² = πr(l + r), where r is the base radius and l is the slant height. This includes both curved surface and circular base area.

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Given: r = 7 cm, h = 24 cm. First find slant height: l = √(r² + h²) = √(49 + 576) = √625 = 25 cm. Curved Surface Area = πrl = π × 7 × 25 = 175π = 550 cm² (taking π = 22/7)…

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A sphere is a 3D solid figure made up of all points in space at a constant distance (radius) from a fixed point (center). A circle is a 2D plane figure. When a circular disc is rotated about its diame…

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Surface Area of a Sphere = 4πr², where r is the radius. This is equivalent to 4 times the area of a circle with the same radius.

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A hemisphere is half of a sphere, formed by cutting a sphere through its center. Curved Surface Area = 2πr². Total Surface Area = 3πr² (includes curved surface + flat circular base).