{
  "title": "Frustum of a Cone (Surface Areas and Volumes) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A frustum is obtained by cutting a cone with a plane:", "options": {"A": "Parallel to base", "B": "Perpendicular to base", "C": "At an angle", "D": "Through vertex"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "In a frustum, the two circular faces are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting", "D": "Oblique"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "If R and r are radii of circular faces of frustum, and h is height, volume formula is:", "options": {"A": "(πh/3)(R² + r² + Rr)", "B": "πh(R² + r²)", "C": "(πh/2)(R + r)²", "D": "π(R² - r²)h"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "The slant height of frustum l =", "options": {"A": "√[h² + (R - r)²]", "B": "h + (R - r)", "C": "√(h² + R²)", "D": "√(h² + r²)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Curved surface area of frustum =", "options": {"A": "πl(R + r)", "B": "π(R² + r²)", "C": "2πh(R + r)", "D": "π(R + r)²"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Total surface area of frustum includes:", "options": {"A": "CSA + πR² + πr²", "B": "CSA only", "C": "πR² + πr² only", "D": "CSA + 2π(R² + r²)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If frustum is from cone of height H and radius R, and small cone height = h, then r/R =", "options": {"A": "h/H", "B": "H/h", "C": "h²/H²", "D": "H²/h²"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "A bucket is usually shaped like:", "options": {"A": "Frustum of cone", "B": "Cone", "C": "Cylinder", "D": "Sphere"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If R = r in frustum, it becomes:", "options": {"A": "Cylinder", "B": "Cone", "C": "Sphere", "D": "Cube"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "For frustum from cone, height of frustum =", "options": {"A": "H - h", "B": "H + h", "C": "H × h", "D": "H/h"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If frustum height is zero, it becomes:", "options": {"A": "Annulus (ring)", "B": "Cone", "C": "Circle", "D": "Cylinder"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Volume of frustum is _____ volume of original cone minus volume of small cone.", "options": {"A": "Equal to", "B": "Less than", "C": "Greater than", "D": "Half of"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "In frustum formula, l represents:", "options": {"A": "Slant height", "B": "Length", "C": "Lateral height", "D": "Linear height"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "For frustum with R=8cm, r=4cm, h=3cm, l =", "options": {"A": "5cm", "B": "4cm", "C": "6cm", "D": "7cm"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "If cone is cut at midpoint parallel to base, R:r =", "options": {"A": "2:1", "B": "1:1", "C": "3:1", "D": "4:1"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "CSA of frustum formula doesn't depend on:", "options": {"A": "Individual R and r separately", "B": "Sum R+r", "C": "Slant height", "D": "π"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "When viewing frustum from side, shape is:", "options": {"A": "Trapezium", "B": "Triangle", "C": "Rectangle", "D": "Square"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "If R=10cm, r=6cm, then (R - r) =", "options": {"A": "4cm", "B": "16cm", "C": "8cm", "D": "2cm"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "For calculating paint needed for bucket, we need:", "options": {"A": "TSA", "B": "Volume", "C": "Only CSA", "D": "Only base areas"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If frustum made of metal, weight =", "options": {"A": "Volume × density", "B": "Surface area × density", "C": "Height × density", "D": "(R+r) × density"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Frustum has R=14cm, r=7cm, h=24cm. Slant height l =", "options": {"A": "25cm", "B": "24cm", "C": "26cm", "D": "23cm"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Volume of frustum with R=10cm, r=4cm, h=12cm:", "options": {"A": "1744π cm³ ≈ 5478.8cm³", "B": "1200π cm³", "C": "1560π cm³", "D": "1920π cm³"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "CSA of frustum with R=8cm, r=3cm, l=13cm:", "options": {"A": "143π cm² ≈ 449.1cm²", "B": "130π cm²", "C": "156π cm²", "D": "169π cm²"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "TSA of frustum with R=9cm, r=4cm, l=12cm:", "options": {"A": "π(156 + 81 + 16) = 253π cm²", "B": "240π cm²", "C": "260π cm²", "D": "280π cm²"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Frustum from cone of height 27cm, radius 9cm cut at 12cm from vertex. Volume of frustum:", "options": {"A": "(π/3)×12×(81+9+27) = 468π cm³", "B": "432π cm³", "C": "504π cm³", "D": "540π cm³"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "If frustum volume = 5929π/3 cm³, h=21cm, R=14cm, find r.", "options": {"A": "7cm", "B": "8cm", "C": "6cm", "D": "5cm"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Slant height of frustum with h=15cm, R-r=8cm:", "options": {"A": "17cm", "B": "15cm", "C": "20cm", "D": "12cm"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Frustum CSA = 4070cm², l=37cm, R+r =", "options": {"A": "35cm", "B": "37cm", "C": "40cm", "D": "32cm"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Bucket shaped frustum: R=15cm, r=5cm, h=24cm. Capacity in liters:", "options": {"A": "5.72 liters", "B": "6.28 liters", "C": "7.15 liters", "D": "4.85 liters"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Frustum TSA = 2145π cm², R=20cm, r=8cm, l=?", "options": {"A": "25cm", "B": "20cm", "C": "30cm", "D": "35cm"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Original cone height=45cm, radius=15cm. Cut at 15cm from vertex. Volume of frustum:", "options": {"A": "26250π/3 cm³", "B": "8750π cm³", "C": "13125π cm³", "D": "17500π/3 cm³"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Frustum l=10cm, R=7cm, r=3cm. Height h =", "options": {"A": "8cm", "B": "6cm", "C": "9cm", "D": "7cm"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Metal bucket (frustum) with R=14cm, r=8cm, h=21cm. Metal sheet area needed:", "options": {"A": "TSA = π[22×25 + 196 + 64] = 2530π cm²", "B": "2400π cm²", "C": "2600π cm²", "D": "2700π cm²"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Frustum volume 1232cm³, h=6cm, R=10cm. Find r.", "options": {"A": "6cm", "B": "5cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Cone of height 16cm, radius 6cm cut at 4cm from vertex. CSA of frustum:", "options": {"A": "π×10.77×(6+1.5)=80.78π cm²", "B": "75π cm²", "C": "85π cm²", "D": "90π cm²"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Frustum with R=12cm, r=9cm, l=5cm. Volume (h found first):", "options": {"A": "h=4cm, V=π/3×4×(144+81+108)=444π cm³", "B": "400π cm³", "C": "500π cm³", "D": "600π cm³"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Bucket holds 28.49 liters. R=20cm, r=10cm. Height:", "options": {"A": "24cm", "B": "20cm", "C": "30cm", "D": "25cm"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Frustum TSA = 748π cm². R=10cm, r=6cm, l=14cm. Check consistency.", "options": {"A": "TSA=π[14×16+100+36]=π[224+136]=360π ≠ 748π", "B": "Consistent", "C": "Can't determine", "D": "Data insufficient"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Cone height 30cm, radius 10cm. Cut parallel to base at height h to get frustum volume = 1/3 of original cone. h =", "options": {"A": "10∛2 ≈ 12.6cm", "B": "15cm", "C": "20cm", "D": "10cm"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Frustum l=26cm, h=24cm, r=5cm. Find R.", "options": {"A": "10cm", "B": "12cm", "C": "15cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Volume of frustum = 259π cm³, h=7cm, R=8cm, r=4cm. Verify.", "options": {"A": "V=π/3×7×(64+16+32)=π/3×7×112=261.33π ≈ close", "B": "Exact", "C": "Not correct", "D": "Can't verify"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Frustum made of iron weighing 7.8g/cm³. R=12cm, r=8cm, h=9cm. Weight:", "options": {"A": "V=π/3×9×(144+64+96)=912π≈2865cm³, weight=22.35kg", "B": "20kg", "C": "25kg", "D": "18kg"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Cone cut into frustum and small cone. If small cone volume: frustum volume = 1:7, height ratio small:original =", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "1:√8"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Frustum CSA = 1650cm², R=15cm, r=10cm. Slant height:", "options": {"A": "21cm", "B": "20cm", "C": "22cm", "D": "25cm"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Bucket (frustum) without lid. R=14cm, r=7cm, h=15cm. Metal area:", "options": {"A": "CSA+πr²=π×25×21+49π=525π+49π=574π cm²", "B": "600π cm²", "C": "550π cm²", "D": "500π cm²"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Frustum height 8cm, volume 504π cm³, R=9cm. Find r.", "options": {"A": "6cm", "B": "5cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Cone of height 36cm cut at 12cm from base. Ratio of volumes (top:bottom):", "options": {"A": "1:26", "B": "1:8", "C": "1:27", "D": "1:7"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Frustum l=17cm, R-r=8cm. Height h =", "options": {"A": "15cm", "B": "12cm", "C": "16cm", "D": "14cm"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "TSA of frustum 858π cm², l=13cm, R=12cm. Find r.", "options": {"A": "5cm", "B": "6cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Frustum from cone radius 21cm, height 28cm cut at 7cm from vertex. Volume:", "options": {"A": "4851π cm³", "B": "5000π cm³", "C": "4500π cm³", "D": "5200π cm³"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Bucket capacity 13.572 liters. R=12cm, r=6cm. Find height.", "options": {"A": "28cm", "B": "24cm", "C": "30cm", "D": "32cm"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Frustum CSA = 1760cm², l=20cm. R+r =", "options": {"A": "28cm", "B": "30cm", "C": "25cm", "D": "32cm"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Cone height 40cm, radius 10cm. Cut to get frustum of height 24cm. Volume of frustum:", "options": {"A": "5888π/3 cm³", "B": "6000π/3 cm³", "C": "5500π/3 cm³", "D": "6200π/3 cm³"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Frustum with h=9cm, volume=333π cm³, r=4cm. Find R.", "options": {"A": "7cm", "B": "6cm", "C": "8cm", "D": "9cm"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Cone cut into two parts through mid-point parallel to base. Ratio of CSA of frustum to small cone:", "options": {"A": "3:1", "B": "4:1", "C": "2:1", "D": "5:1"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Frustum l=25cm, h=24cm, R=10cm. Find r.", "options": {"A": "2cm", "B": "3cm", "C": "4cm", "D": "5cm"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "TSA of frustum 1199π cm², R=14cm, r=7cm. Find l.", "options": {"A": "25cm", "B": "20cm", "C": "22cm", "D": "24cm"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Frustum volume = 1099π cm³, h=7cm, R=10cm, r=7cm. Verify.", "options": {"A": "V=π/3×7×(100+49+70)=π/3×7×219=511π ≠ 1099π", "B": "Correct", "C": "Approximately correct", "D": "Data wrong"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Bucket holds 18.15 liters. R=15cm, r=9cm. Height:", "options": {"A": "20cm", "B": "22cm", "C": "24cm", "D": "18cm"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Cone height 27cm cut at 9cm from vertex. Ratio of CSA of frustum to original cone:", "options": {"A": "8:9", "B": "2:3", "C": "5:9", "D": "7:9"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Frustum with R=8cm, r=5cm, l=5cm. Volume:", "options": {"A": "h=4cm, V=π/3×4×(64+25+40)=172π cm³", "B": "180π cm³", "C": "160π cm³", "D": "200π cm³"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Metal frustum weighs 15.4kg (density 7.7g/cm³). R=14cm, r=7cm. Height:", "options": {"A": "20cm", "B": "18cm", "C": "22cm", "D": "24cm"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Cone cut so that frustum volume = 7/8 original volume. Cut at what fraction from vertex?", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "2/3"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Frustum CSA = 135π cm², l=9cm, R=8cm. Find r.", "options": {"A": "7cm", "B": "6cm", "C": "5cm", "D": "4cm"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Bucket without lid: CSA=1925cm², R=14cm, r=7cm. Height:", "options": {"A": "24cm", "B": "20cm", "C": "22cm", "D": "18cm"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Frustum volume 1232cm³, h=6cm, R=10cm, r=?", "options": {"A": "6cm", "B": "5cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Cone radius 12cm, height 16cm cut at 4cm from vertex. TSA of frustum:", "options": {"A": "π[15×27+144+9]=π[405+153]=558π cm²", "B": "600π cm²", "C": "500π cm²", "D": "550π cm²"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Frustum l=13cm, h=12cm, r=3cm. Find R.", "options": {"A": "8cm", "B": "9cm", "C": "10cm", "D": "7cm"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "TSA of frustum 704π cm², l=10cm, r=6cm. Find R.", "options": {"A": "10cm", "B": "12cm", "C": "14cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Frustum volume 567π cm³, h=9cm, r=5cm. Find R.", "options": {"A": "8cm", "B": "7cm", "C": "9cm", "D": "10cm"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Cone height 30cm, volume 3000π cm³. Cut to get frustum of volume 2960π cm³. Height of frustum:", "options": {"A": "29cm", "B": "28cm", "C": "27cm", "D": "26cm"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Bucket capacity 9.24 liters. R=12cm, h=14cm. Find r.", "options": {"A": "6cm", "B": "7cm", "C": "8cm", "D": "5cm"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Frustum CSA = 220π cm², R+r=20cm. Slant height:", "options": {"A": "11cm", "B": "10cm", "C": "12cm", "D": "15cm"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Cone cut so that frustum CSA = 3/4 original cone CSA. Cut at what height ratio?", "options": {"A": "1/2 from vertex", "B": "1/3 from vertex", "C": "2/3 from vertex", "D": "3/4 from vertex"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Frustum h=16cm, volume=2624π/3 cm³, R=12cm. Find r.", "options": {"A": "8cm", "B": "7cm", "C": "9cm", "D": "10cm"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Metal bucket (no lid) weighs 2kg (density 8g/cm³). R=10cm, r=6cm, h=14cm. Check consistency.", "options": {"A": "V=π/3×14×(100+36+60)=π/3×14×196≈2870cm³, weight≈23kg ≠ 2kg", "B": "Consistent", "C": "Approximately consistent", "D": "Can't determine"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Cone radius 15cm, height 20cm. Cut parallel to base to get frustum of height 12cm. Volume of frustum:", "options": {"A": "2772π cm³", "B": "3000π cm³", "C": "2500π cm³", "D": "3200π cm³"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Frustum l=17cm, R-r=8cm, h=15cm. Verify l.", "options": {"A": "l=√(225+64)=17cm ✓", "B": "l should be 16cm", "C": "l should be 18cm", "D": "Data inconsistent"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "TSA of frustum 384π cm², R=10cm, r=6cm. Find h.", "options": {"A": "8cm", "B": "6cm", "C": "10cm", "D": "12cm"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Frustum volume 259π cm³, h=3cm, r=4cm. Find R.", "options": {"A": "9cm", "B": "8cm", "C": "10cm", "D": "7cm"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "The slant height of frustum of cone is 4cm and perimeters of circular ends are 18cm and 6cm. Find CSA.", "options": {"A": "48cm²", "B": "36cm²", "C": "24cm²", "D": "54cm²"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "A fez, cap used by Turks, is shaped like frustum. If radii 10cm and 4cm, height 15cm, find area of material used.", "options": {"A": "710π cm²", "B": "680π cm²", "C": "750π cm²", "D": "800π cm²"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "A container made of metal sheet is in form of frustum with radii 8cm and 4cm, height 6cm. Find cost of milk at ₹20/liter if full.", "options": {"A": "₹10.56", "B": "₹12.50", "C": "₹15.00", "D": "₹18.00"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "A bucket is 32cm high with radii 18cm and 8cm. Find capacity in liters.", "options": {"A": "12.16 liters", "B": "15.00 liters", "C": "10.50 liters", "D": "18.25 liters"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Frustum of right circular cone has radii 5cm and 9cm, height 12cm. Find TSA.", "options": {"A": "298π cm²", "B": "320π cm²", "C": "350π cm²", "D": "280π cm²"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "A cone of height 24cm and radius 6cm cut into two parts by plane through mid-point parallel to base. Find ratio of volumes of two parts.", "options": {"A": "1:7", "B": "1:8", "C": "1:3", "D": "1:5"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Milk in container (frustum) with radii 15cm and 10cm, height 30cm poured into cylindrical vessel radius 10cm. Find height in cylinder.", "options": {"A": "47.5cm", "B": "50cm", "C": "45cm", "D": "55cm"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "A bucket open at top made of metal sheet. Radii 25cm and 15cm, height 40cm. Find area of metal sheet.", "options": {"A": "4325π cm²", "B": "4500π cm²", "C": "4000π cm²", "D": "4800π cm²"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Frustum volume is 1/3 of cone from which cut. If cone height 27cm, find height of frustum.", "options": {"A": "19cm", "B": "18cm", "C": "20cm", "D": "21cm"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "A drinking glass shape frustum height 14cm, diameters 4cm and 2cm. Find capacity.", "options": {"A": "102.67π cm³", "B": "110π cm³", "C": "95π cm³", "D": "120π cm³"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "From solid cone of height 15cm, base radius 9cm, frustum made by cutting with plane parallel to base so that volumes of frustum and remaining cone are equal. Find height of frustum.", "options": {"A": "15(1-1/∛2) ≈ 5.5cm", "B": "7.5cm", "C": "10cm", "D": "12cm"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "A container frustum shaped has radii 20cm and 8cm, height 16cm full of water. Water poured into cylindrical vessel radius 10cm. Find height.", "options": {"A": "19.84cm", "B": "20cm", "C": "18cm", "D": "22cm"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "The perimeters of ends of frustum are 48cm and 36cm. If slant height 5cm, find CSA.", "options": {"A": "210cm²", "B": "180cm²", "C": "240cm²", "D": "200cm²"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "A bucket made of aluminum sheet weighs 500g. If thickness negligible, radii 14cm and 7cm, height 15cm, density 2.7g/cm³, find if data consistent.", "options": {"A": "Volume=2695π cm³≈8465cm³, weight≈22.85kg ≠ 500g", "B": "Consistent", "C": "Approximately consistent", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Frustum CSA equal to sum of areas of two circular ends. If R=9cm, r=4cm, find slant height.", "options": {"A": "13cm", "B": "12cm", "C": "15cm", "D": "10cm"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "A cone cut into two parts by plane parallel to base. If CSA of frustum is 5/9 of original cone CSA, find ratio of heights of small cone to original cone.", "options": {"A": "2:3", "B": "1:2", "C": "3:4", "D": "4:5"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "From solid cone of height 12cm, base radius 6cm, conical cavity of same height, base radius 3cm made. Find TSA of remaining solid.", "options": {"A": "117π cm²", "B": "120π cm²", "C": "125π cm²", "D": "130π cm²"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "A metallic frustum melted to form sphere of radius 6cm. If frustum radii 8cm and 4cm, height 12cm, find if possible.", "options": {"A": "Sphere volume=288π, frustum volume=448π, not possible", "B": "Possible", "C": "Exactly possible", "D": "Need more data"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "The difference of radii of ends of frustum is 7cm. If slant height 25cm, height 24cm, find radii.", "options": {"A": "R=20cm, r=13cm", "B": "R=18cm, r=11cm", "C": "R=25cm, r=18cm", "D": "R=22cm, r=15cm"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "A shuttle cock for badminton has frustum shape with radii 3cm and 1cm, height 4cm mounted on hemisphere of radius 1cm. Find TSA.", "options": {"A": "π(20+1+1)=22π cm²", "B": "25π cm²", "C": "20π cm²", "D": "28π cm²"}, "correct_answer": "A"}
  ]
}