{
  "title": "Conversion of Solid Shapes - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "When a solid melts and recasts, what remains same? ♻️", "options": {"A": "Volume", "B": "Surface area", "C": "Shape", "D": "Weight"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Sphere melted into cylinder: Volume ? 🔄", "options": {"A": "Stays same", "B": "Increases", "C": "Decreases", "D": "Doubles"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Cone recast into cylinder: Which changes? 📦", "options": {"A": "Surface area", "B": "Volume", "C": "Material", "D": "Density"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Cube melted into sphere: Process called? 🧊➡️⚫", "options": {"A": "Recasting", "B": "Cutting", "C": "Painting", "D": "Measuring"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Cylinder melted into cones: Number found by? 🔢", "options": {"A": "Volume division", "B": "Surface division", "C": "Height division", "D": "Radius division"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Sphere radius r melted into cube. Side of cube? 📐", "options": {"A": "∛[(4/3)πr³]", "B": "√(4πr²)", "C": "πr³", "D": "r³"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "When recasting, material is: 🏗️", "options": {"A": "Conserved", "B": "Lost", "C": "Gained", "D": "Changed"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Cone melted into sphere: Formula connection? 🔺➡️🔵", "options": {"A": "(1/3)πr²h = (4/3)πR³", "B": "πr²h = 4πR²", "C": "πrl = 4πR²", "D": "r+h = R"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Cylinder melted into 2 spheres: Volume relation? 🛢️➡️⚫⚫", "options": {"A": "Cyl vol = 2 × Sphere vol", "B": "Cyl vol = Sphere vol", "C": "Cyl SA = Sphere SA", "D": "Cyl height = Sphere diam"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which cannot change during recasting? 🚫", "options": {"A": "Mass", "B": "Shape", "C": "Surface", "D": "Color"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Cuboid melted into cylinder: What's equal? 📦➡️🛢️", "options": {"A": "Volumes", "B": "Heights", "C": "Widths", "D": "Surfaces"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Metalsmith melts jewelry to make new: Process? 👨‍🏭", "options": {"A": "Recasting", "B": "Cutting", "C": "Polishing", "D": "Designing"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Sphere to wire (cylinder): Volume? ⚫➡️🧵", "options": {"A": "Same", "B": "Wire has more", "C": "Sphere has more", "D": "Half"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Cone to hemisphere: If radius same, cone height? 🔺➡️🌓", "options": {"A": "2r", "B": "r", "C": "3r", "D": "r/2"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Cube side 4cm to sphere. Sphere radius? 🧊➡️🔵", "options": {"A": "∛(64×3/4π)", "B": "4 cm", "C": "2 cm", "D": "8 cm"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Cylinder to cone: If radius same, height ratio? 🛢️➡️🔺", "options": {"A": "Cyl height = 3×Cone height", "B": "Equal", "C": "Cone=2×Cyl", "D": "Cone=½×Cyl"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Recasting assumes no: ⚠️", "options": {"A": "Material loss", "B": "Shape change", "C": "Volume change", "D": "Temperature change"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Sphere radius 3cm to cylinder radius 2cm. Find height? 🔄", "options": {"A": "(4/3)π×3³ = π×2²×h", "B": "4π×3² = 2π×2×h", "C": "3=2+h", "D": "3²=2²+h²"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Cone melted into smaller cones: Number? 🔺➡️🔺🔺", "options": {"A": "Large vol ÷ Small vol", "B": "Large SA ÷ Small SA", "C": "Large height ÷ Small height", "D": "Large radius ÷ Small radius"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Cylinder to wire: Wire is long cylinder with small: 🧵", "options": {"A": "Radius", "B": "Volume", "C": "Surface area", "D": "Density"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Cylinder radius 6cm, height 15cm melted into spheres radius 3cm. How many spheres? 🎯", "options": {"A": "(π×6²×15) ÷ [(4/3)π×3³]", "B": "(2π×6×15) ÷ (4π×3²)", "C": "15 ÷ 6", "D": "6² ÷ 3²"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Cone radius 9cm, height 12cm recast into cylinder radius 6cm. Cylinder height? 📐", "options": {"A": "[(1/3)×9²×12] ÷ 6²", "B": "[9×12] ÷ 6", "C": "√(9²+12²) ÷ 6", "D": "(9+12) ÷ 2"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Sphere radius 10cm melted into cones radius 5cm, height 12cm. Number of cones? 🍦", "options": {"A": "[(4/3)×10³] ÷ [(1/3)×5²×12]", "B": "[4×10²] ÷ [5×12]", "C": "10³ ÷ 5³", "D": "10 ÷ 5"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Cuboid 22cm×18cm×4cm melted into cylinder radius 7cm. Height? 📦", "options": {"A": "(22×18×4) ÷ (π×7²)", "B": "(22+18+4) ÷ (2π×7)", "C": "√(22²+18²) ÷ 7", "D": "22×18 ÷ (π×7)"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Cylinder radius 14cm, height 20cm to spheres radius 7cm. How many? ⚫", "options": {"A": "(14²×20) ÷ [(4/3)×7³]", "B": "(14×20) ÷ 7", "C": "20 ÷ 14", "D": "14² ÷ 7²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Metallic sphere radius 8.4cm melted into cylinder radius 12cm. Cylinder height? 🔄", "options": {"A": "[(4/3)×8.4³] ÷ 12²", "B": "[4×8.4²] ÷ (2×12)", "C": "8.4³ ÷ 12³", "D": "8.4 ÷ 12"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Cone radius 5cm, height 12cm to hemisphere. Hemisphere radius? 🌓", "options": {"A": "∛[(1/3)×5²×12 × 3/2]", "B": "√[(5²+12²) ÷ 2]", "C": "5+12 ÷ 2", "D": "5 cm"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Cylinder radius 3.5cm, height 10cm to wire radius 0.5cm. Wire length? 🧵", "options": {"A": "(3.5²×10) ÷ 0.5²", "B": "(3.5×10) ÷ 0.5", "C": "10 ÷ 0.5", "D": "3.5 ÷ 0.5"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Cube side 21cm melted into cone radius 7cm. Cone height? 🧊➡️🔺", "options": {"A": "(21³ × 3) ÷ 7²", "B": "21³ ÷ 7²", "C": "21 ÷ 7", "D": "21² ÷ 7²"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Sphere radius 6cm to cones radius 3cm, height 4cm. Number? 📊", "options": {"A": "[(4/3)×6³] ÷ [(1/3)×3²×4]", "B": "[6³] ÷ [3²×4]", "C": "[4×6²] ÷ [3×4]", "D": "6 ÷ 3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Cylinder radius 10cm, height 15cm to spheres radius 5cm. Spheres count? 🎲", "options": {"A": "(10²×15) ÷ [(4/3)×5³]", "B": "(10×15) ÷ 5", "C": "15 ÷ 10", "D": "10² ÷ 5²"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Cone radius 7cm, height 24cm to cylinder radius 14cm. Height? 📏", "options": {"A": "[(1/3)×7²×24] ÷ 14²", "B": "[7×24] ÷ 14", "C": "√(7²+24²) ÷ 14", "D": "24 ÷ 2"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Sphere radius 9cm melted into cube. Cube side? 🔲", "options": {"A": "∛[(4/3)×9³]", "B": "√(4×9²)", "C": "9×2", "D": "9÷2"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Cylinder radius 4cm, height 18cm to cones radius 3cm, height 4cm. Cones count? 🗻", "options": {"A": "(4²×18) ÷ [(1/3)×3²×4]", "B": "(4×18) ÷ (3×4)", "C": "18 ÷ 4", "D": "4² ÷ 3²"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Hemisphere radius 14cm to cone radius 7cm. Cone height? 🌓➡️🔺", "options": {"A": "[(2/3)×14³ × 3] ÷ 7²", "B": "[14³] ÷ 7²", "C": "14 ÷ 7", "D": "14² ÷ 7²"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Cuboid 16cm×11cm×8cm to cylinder radius 7cm. Height? 🔄", "options": {"A": "(16×11×8) ÷ (π×7²)", "B": "(16+11+8) ÷ (2π×7)", "C": "√(16²+11²) ÷ 7", "D": "16×11 ÷ (π×7)"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Sphere radius 5cm to wire radius 0.25cm. Length? 📏", "options": {"A": "[(4/3)×5³] ÷ (0.25²)", "B": "[4×5²] ÷ (2×0.25)", "C": "5³ ÷ 0.25³", "D": "5 ÷ 0.25"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Cone radius 6cm, height 8cm to sphere. Sphere radius? 🔵", "options": {"A": "∛[(1/3)×6²×8 × 3/4]", "B": "√(6²+8²) ÷ 2", "C": "(6+8) ÷ 2", "D": "6 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Cylinder radius 10cm, height 21cm to cones radius 7cm, height 12cm. Number? 🔢", "options": {"A": "(10²×21) ÷ [(1/3)×7²×12]", "B": "(10×21) ÷ (7×12)", "C": "21 ÷ 12", "D": "10² ÷ 7²"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Cube side 12cm to hemisphere. Radius? 🌓", "options": {"A": "∛[(12³ × 3)/(2π)]", "B": "√(12²/2)", "C": "12/2", "D": "12 cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Sphere radius 9cm melted into cones radius 3cm, height 4cm. If 10% material wasted, cones made? 🗑️", "options": {"A": "0.9 × [(4/3)×9³] ÷ [(1/3)×3²×4]", "B": "[(4/3)×9³] ÷ [(1/3)×3²×4]", "C": "1.1 × [same]", "D": "[same] ÷ 0.9"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Cylinder radius 7cm, height 10cm to cones. If each cone uses 154 cm³, how many? 📊", "options": {"A": "(π×7²×10) ÷ 154", "B": "(2π×7×10) ÷ 154", "C": "(7²×10) ÷ 154", "D": "(7×10) ÷ 154"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Cone radius 6cm, height 8cm to cylinder of same height. Cylinder radius? 🔄", "options": {"A": "√[(1/3)×6²×8 ÷ 8]", "B": "6 ÷ √3", "C": "6 cm", "D": "8 cm"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Hemisphere radius 10.5cm to cones radius 3.5cm, height 3cm. Number with 5% waste? ⚠️", "options": {"A": "0.95 × [(2/3)×10.5³] ÷ [(1/3)×3.5²×3]", "B": "[same] without 0.95", "C": "1.05 × [same]", "D": "[same] ÷ 0.95"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "Cuboid 44cm×21cm×12cm to spheres radius 7cm. Maximum spheres? 🎯", "options": {"A": "Floor[(44×21×12) ÷ ((4/3)×7³)]", "B": "Ceiling[same]", "C": "44×21×12 ÷ sphere vol", "D": "Round[same]"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Cylinder melted into sphere. If cylinder radius = height = h, sphere radius? 🔄", "options": {"A": "∛[(3/4)h³]", "B": "h", "C": "h/2", "D": "√(3/2)h"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Cone radius R, height H melted into cylinder radius r. Height ratio H/h? 📐", "options": {"A": "(3r²)/(R²)", "B": "(R²)/(3r²)", "C": "R/r", "D": "r/R"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Wire length 1km, radius 0.7mm drawn into wire radius 0.5mm. New length? 📏", "options": {"A": "(0.7² × 1000) ÷ 0.5² meters", "B": "(0.7 × 1000) ÷ 0.5", "C": "1000 × 0.7 ÷ 0.5", "D": "1000 × 0.5² ÷ 0.7²"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Sphere radius 6cm to cones. If cone height = radius = 3cm, how many? 🍦", "options": {"A": "[(4/3)×6³] ÷ [(1/3)×3³]", "B": "[6³] ÷ [3³]", "C": "[4×6²] ÷ [3²]", "D": "6 ÷ 3"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Cylinder radius 10cm, height 30cm to cones radius 5cm, height 10cm. If 8% waste, cones? 🏭", "options": {"A": "0.92 × (π×10²×30) ÷ [(1/3)π×5²×10]", "B": "1.08 × [same]", "C": "[same] without factor", "D": "[same] ÷ 0.92"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Cube side 8cm melted into spheres radius 1cm. How many complete spheres? 🔲➡️⚫⚫", "options": {"A": "Floor[8³ ÷ ((4/3)π×1³)]", "B": "Ceiling[same]", "C": "8³ ÷ sphere vol", "D": "Round[same]"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Cone radius 12cm, height 5cm to hemisphere. Hemisphere radius? 🌓", "options": {"A": "∛[(1/3)×12²×5 × 3/2]", "B": "√(12²+5²) ÷ 2", "C": "(12+5) ÷ 2", "D": "12 cm"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Cylinder to cone: If heights equal, radius ratio? 📊", "options": {"A": "r_cylinder = r_cone/√3", "B": "r_cylinder = √3 r_cone", "C": "Equal", "D": "r_cone = 3 r_cylinder"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Metallic sphere radius 15cm drawn into wire radius 0.3cm. Wire length? 🧵", "options": {"A": "[(4/3)×15³] ÷ (0.3²)", "B": "[4×15²] ÷ (2×0.3)", "C": "15³ ÷ 0.3³", "D": "15 ÷ 0.3"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Cuboid 50cm×44cm×20cm to cones radius 7cm, height 24cm. Number? 🏗️", "options": {"A": "(50×44×20) ÷ [(1/3)×7²×24]", "B": "(50+44+20) ÷ (7+24)", "C": "√(50²+44²) ÷ 7", "D": "50×44 ÷ (π×7)"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Sphere radius 14cm to cylinders radius 7cm, height 6cm. Cylinders count? 🛢️", "options": {"A": "[(4/3)×14³] ÷ (π×7²×6)", "B": "[4×14²] ÷ (2π×7×6)", "C": "14³ ÷ 7³", "D": "14 ÷ 7"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Cone melted into 2 equal cones. Each new cone volume? 🔺➡️🔺🔺", "options": {"A": "Half of original", "B": "Same as original", "C": "Double original", "D": "Quarter original"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Cylinder radius 21cm, height 25cm to spheres. If sphere SA = 616 cm², find radius then count. 📐", "options": {"A": "Solve 4πR²=616, then (π×21²×25) ÷ ((4/3)πR³)", "B": "21²×25 ÷ sphere vol", "C": "Use R=21", "D": "25÷ diameter"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Cuboid 24cm×18cm×8cm to cylinders radius 6cm. If height = 4cm, number? 🔢", "options": {"A": "(24×18×8) ÷ (π×6²×4)", "B": "(24+18+8) ÷ (6+4)", "C": "24×18 ÷ (π×6²)", "D": "8÷4"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Sphere to cube: If cube diagonal = 12√3 cm, sphere radius? 🔍", "options": {"A": "Solve: (4/3)πR³ = (diag/√3)³", "B": "R = diagonal/2", "C": "R = 12 cm", "D": "R = 6 cm"}, "correct_answer": "A"}
  ]
}