Solids

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A pyramid is a solid with a polygonal base and triangular faces meeting at a single point called the apex. Key components: • Base edges: sides of the polygonal base • Lateral edges: edges of triangula…

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Step 1: Calculate base area Base area = 10² = 100 cm² Step 2: Find slant height using Pythagoras theorem Slant height = √(13² - 5²) = √(169 - 25) = √144 = 12 cm (Note: 5 cm is half of base edge) Ste…

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In any square pyramid, there exists a right triangle where: • One leg = height of pyramid (h) • Second leg = half the base edge (a/2) • Hypotenuse = lateral edge (l) • Slant height (s) = height of tri…

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Formula: Volume of pyramid = ⅓ × base area × height Step 1: Calculate base area Base area = 12² = 144 cm² Step 2: Apply volume formula Volume = ⅓ × 144 × 8 = ⅓ × 1152 = 384 cm³ Key concept: Volume …

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Step 1: Calculate volume of cube Volume of cube = 15³ = 3375 cm³ Step 2: Set up equation for pyramid Volume of pyramid = Volume of cube (conservation of material) ⅓ × base area × height = 3375 Step …

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A cone is a pyramid-like solid with a circular base instead of a polygonal base. Key similarities and differences: Similarities: • Both have an apex (tip) • Both have a height (perpendicular distance…

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Step 1: Identify given information • Original circle radius = 15 cm • Central angle = 120° = ⅓ of 360° Step 2: Find slant height Slant height = radius of original circle = 15 cm Step 3: Calculate ar…

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Formula: Curved Surface Area = πrl where r = base radius, l = slant height Derivation: When cone is unfolded, we get a sector with: • Radius of sector = slant height (l) • Arc length = circumference …