{
  "title": "Sphere Surface Area & Volume - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the formula for the surface area of a sphere? 🌐", "options": {"A": "4πr²", "B": "2πr²", "C": "πr²", "D": "4/3 πr³"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "If radius of a sphere is 7 cm, what is its surface area? (π = 22/7)", "options": {"A": "616 cm²", "B": "308 cm²", "C": "154 cm²", "D": "1232 cm²"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Volume of a sphere formula is ____. ⚽", "options": {"A": "πr³", "B": "4/3 πr³", "C": "2/3 πr³", "D": "3/4 πr³"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If radius = 3 cm, volume of sphere = ? (π = 3.14)", "options": {"A": "113.04 cm³", "B": "37.68 cm³", "C": "75.36 cm³", "D": "113.04 cm³"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "Surface area of a sphere of radius 10.5 cm? (π = 22/7)", "options": {"A": "1386 cm²", "B": "693 cm²", "C": "2772 cm²", "D": "4158 cm²"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "A sphere has volume 38808 cm³. Its radius is? (π = 22/7)", "options": {"A": "21 cm", "B": "28 cm", "C": "14 cm", "D": "42 cm"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If surface area of a sphere is 154 cm², its radius? (π = 22/7)", "options": {"A": "3.5 cm", "B": "7 cm", "C": "14 cm", "D": "10.5 cm"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Diameter = 14 cm, volume of sphere = ? (π = 22/7)", "options": {"A": "1437.33 cm³", "B": "718.67 cm³", "C": "2156 cm³", "D": "1078 cm³"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Surface area of sphere with diameter 28 cm? (π = 22/7)", "options": {"A": "1232 cm²", "B": "2464 cm²", "C": "616 cm²", "D": "308 cm²"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If volume = 4.19 m³, radius ≈ ? (π = 3.14)", "options": {"A": "1 m", "B": "2 m", "C": "0.5 m", "D": "1.5 m"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Sphere radius doubled, surface area becomes ____ times. 🔴🔴", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Two spheres radii ratio 2:3, surface areas ratio? 📏", "options": {"A": "2:3", "B": "4:9", "C": "8:27", "D": "3:2"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Half of a sphere is called a ____.", "options": {"A": "Cone", "B": "Hemisphere", "C": "Semicircle", "D": "Spheroid"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Surface area of hemisphere of radius r = ____.", "options": {"A": "2πr²", "B": "3πr²", "C": "4πr²", "D": "(4/3)πr²"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If r = 7 cm, curved surface area of hemisphere? (π = 22/7)", "options": {"A": "308 cm²", "B": "616 cm²", "C": "154 cm²", "D": "462 cm²"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Volume of hemisphere = ____ of sphere volume.", "options": {"A": "Half", "B": "One-third", "C": "Two-thirds", "D": "Double"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Surface area of a solid hemisphere = ____.", "options": {"A": "2πr²", "B": "3πr²", "C": "πr²", "D": "4πr²"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "A metallic sphere radius 6 cm melted and recast into smaller spheres of radius 2 cm. How many? ♻️", "options": {"A": "9", "B": "18", "C": "27", "D": "36"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "If volume of sphere is 36π cm³, its surface area is? 📦", "options": {"A": "24π cm²", "B": "36π cm²", "C": "48π cm²", "D": "12π cm²"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "A sphere fits exactly in a cube of side 10 cm. Sphere's radius = ?", "options": {"A": "5 cm", "B": "10 cm", "C": "7.5 cm", "D": "2.5 cm"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "If surface area of sphere is 616 cm², find its volume. (π = 22/7)", "options": {"A": "1437.33 cm³", "B": "1796.67 cm³", "C": "718.67 cm³", "D": "2156 cm³"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Two spheres have volumes in ratio 64:27. Their radii ratio? 🔢", "options": {"A": "16:9", "B": "8:3", "C": "4:3", "D": "64:27"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "A hemispherical bowl radius 5 cm, its curved surface area? (π = 3.14)", "options": {"A": "78.5 cm²", "B": "157 cm²", "C": "235.5 cm²", "D": "314 cm²"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Total surface area of solid hemisphere radius 3.5 cm? (π = 22/7)", "options": {"A": "115.5 cm²", "B": "231 cm²", "C": "173.25 cm²", "D": "57.75 cm²"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If volume of a sphere is 4851 cm³, its radius? (π = 22/7)", "options": {"A": "10.5 cm", "B": "21 cm", "C": "7 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "The radius of sphere is increased by 20%. Surface area increases by? 📈", "options": {"A": "20%", "B": "40%", "C": "44%", "D": "48.8%"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "A sphere and cube have same volume. If sphere radius is 3 cm, cube side ≈ ?", "options": {"A": "4.84 cm", "B": "5.2 cm", "C": "6 cm", "D": "7.2 cm"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "A hollow sphere outer radius 8 cm, inner radius 7 cm. Volume of metal? (π = 3.14)", "options": {"A": "303.56 cm³", "B": "607.12 cm³", "C": "910.68 cm³", "D": "1214.24 cm³"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "The surface area of a sphere is 1386 cm². Its diameter? (π = 22/7)", "options": {"A": "10.5 cm", "B": "21 cm", "C": "14 cm", "D": "7 cm"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "A hemispherical depression is cut from a cube of side 14 cm. Volume of remaining solid? 🧊", "options": {"A": "2744 cm³", "B": "2156 cm³", "C": "588 cm³", "D": "2420.67 cm³"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "If 3 solid spheres of radii 3,4,5 cm melted to form one sphere, radius of new sphere? ♻️", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "A sphere radius 9 cm, a cylinder radius 9 cm and height 12 cm. Which has greater volume? ⚖️", "options": {"A": "Sphere", "B": "Cylinder", "C": "Equal", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "A sphere's surface area increased from 100π to 400π. Its volume ratio originally to now?", "options": {"A": "1:2", "B": "1:4", "C": "1:8", "D": "1:16"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "A hemispherical bowl holds 0.304 litres water. Its inner radius? (π = 22/7)", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10.5 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "The surface area of a solid hemisphere is 462 cm². Its diameter? (π = 22/7)", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "10.5 cm"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "A sphere radius 5 cm fits inside a cylinder touching all sides. Cylinder volume? 🧂", "options": {"A": "250π cm³", "B": "500π cm³", "C": "375π cm³", "D": "125π cm³"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "A sphere, radius 10 cm, is painted at ₹0.50 per cm². Total cost? (π = 3.14)", "options": {"A": "₹314", "B": "₹628", "C": "₹942", "D": "₹1256"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "A hollow hemisphere total surface area 4158 cm². Outer radius if thickness 1 cm? (π = 22/7)", "options": {"A": "21 cm", "B": "22 cm", "C": "10.5 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If volume of hemisphere is 19404 cm³, its total surface area? (π = 22/7)", "options": {"A": "4158 cm²", "B": "2772 cm²", "C": "1386 cm²", "D": "5544 cm²"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "A sphere volume is 4500π cm³. Find its diameter.", "options": {"A": "30 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "A spherical shell inner radius 4 cm, outer radius 6 cm. Mass if density 7 g/cm³? (π = 3.14) ⚖️", "options": {"A": "1620.64 g", "B": "2025.8 g", "C": "2116.16 g", "D": "1846.32 g"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Three spheres radii 1, 2, 3 cm melted to form one. % increase in surface area from sum of originals? (π common)", "options": {"A": "0%", "B": "10%", "C": "25%", "D": "50%"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "A cylinder radius 7 cm height 10 cm melted into spheres radius 3.5 cm. How many spheres? ♻️", "options": {"A": "6", "B": "9", "C": "12", "D": "15"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "A sphere radius 8 cm is cut into two hemispheres. Total surface area of one hemisphere? 🧠", "options": {"A": "192π cm²", "B": "256π cm²", "C": "320π cm²", "D": "384π cm²"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "A sphere radius R has volume equal to total surface area numerically. R = ?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "hard", "question": "A solid hemisphere radius 10 cm melted into cone radius 10 cm. Height of cone? ♻️", "options": {"A": "10 cm", "B": "15 cm", "C": "20 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "Volume of a sphere is 4.5 m³. Surface area in cm²? (π = 3.14)", "options": {"A": "282600 cm²", "B": "565200 cm²", "C": "141300 cm²", "D": "70650 cm²"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "A sphere radius r fits in a cylinder so cylinder's curved surface area equals sphere's surface area. Cylinder height? 🔄", "options": {"A": "r", "B": "2r", "C": "3r", "D": "4r"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "A metal sphere radius 12 cm melted to form wire radius 2 mm. Length of wire? (π = 3.14)", "options": {"A": "57.6 m", "B": "576 m", "C": "28.8 m", "D": "115.2 m"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Two spheres radii 6 cm & 8 cm melted to form larger sphere. Radius of new sphere? 🔥", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "A hemisphere radius 7 cm surmounted by cone radius 7 cm height 24 cm. Total volume? 🎪", "options": {"A": "1232 cm³", "B": "1848 cm³", "C": "2156 cm³", "D": "2464 cm³"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "If a sphere's radius triples, by what factor does volume increase? 📦", "options": {"A": "3", "B": "9", "C": "18", "D": "27"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "A sphere's surface area 154 cm² is painted at 10 paise per cm². Cost in ₹? (π = 22/7)", "options": {"A": "₹15.4", "B": "₹7.7", "C": "₹30.8", "D": "₹61.6"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Spherical ball radius 3.5 cm dropped in cylindrical vessel radius 7 cm with water. Rise in water level? 🌊", "options": {"A": "0.875 cm", "B": "1.75 cm", "C": "3.5 cm", "D": "7 cm"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "From a cube side 14 cm, largest sphere carved out. Volume removed? (π = 22/7)", "options": {"A": "1437.33 cm³", "B": "1796.67 cm³", "C": "2156 cm³", "D": "2514.67 cm³"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Ratio of surface areas of sphere and circumscribed cube is? 📐", "options": {"A": "π:6", "B": "π:3", "C": "2π:3", "D": "π:2"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "A sphere radius 9 cm, cone radius 9 cm height 27 cm. Ratio of volumes? 🔄", "options": {"A": "2:3", "B": "3:4", "C": "4:9", "D": "2:1"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Hollow sphere external surface area 616 cm², thickness 2 cm. Inner volume? (π = 22/7)", "options": {"A": "179.67 cm³", "B": "1437.33 cm³", "C": "359.33 cm³", "D": "1078 cm³"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "A solid sphere radius 10 cm, cone radius 5 cm height 20 cm. How many cones can be made from sphere? ♻️", "options": {"A": "8", "B": "10", "C": "12", "D": "16"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "A hemisphere radius R is filled with water, poured into cylinder radius R/2. Height of water in cylinder? 🌊", "options": {"A": "4R/3", "B": "8R/3", "C": "2R", "D": "R"}, "correct_answer": "B"}
  ]
}