Q1. The perimeter of a rectangle with length 12 cm and breadth 8 cm is
(a) 20 cm (b) 40 cm (c) 24 cm (d) 32 cm Answer: (b)
Explanation: Perimeter = 2(l + b) = 2(12 + 8) = 2 × 20 = 40 cm.
Q2. The area of a square whose side is 9 m is
(a) 18 m² (b) 36 m² (c) 81 m² (d) 36 m³
Answer: (c)
Explanation: Area = side² = 9² = 81 m².
Q3. The circumference of a circle of radius 7 cm (use π ≈ 22/7) is
(a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
Answer: (a)
Explanation: Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Q4. The area of a triangle with base 10 cm and height 6 cm is
(a) 60 cm² (b) 30 cm² (c) 16 cm² (d) 20 cm²
Answer: (b)
Explanation: Area = ½ × base × height = ½ × 10 × 6 = 30 cm².
Q5. The volume of a cube of edge 5 cm is
(a) 25 cm³ (b) 125 cm³ (c) 150 cm³ (d) 75 cm³
Answer: (b)
Explanation: Volume = edge³ = 5³ = 125 cm³.
Q6. The total surface area of a cylinder with radius 3 cm and height 7 cm (π ≈ 22/7) is
(a) 132 cm² (b) 198 cm² (c) 264 cm² (d) 330 cm²
Answer: (c)
Explanation: TSA = 2πr(r + h) = 2 × (22/7) × 3 × (3 + 7) = (132/7) × 10 = 264 cm².
Q7. The volume of a sphere of radius 4 cm (π ≈ 22/7) is
(a) 268.8 cm³ (b) 213.3 cm³ (c) 102.4 cm³ (d) 85.3 cm³
Answer: (a)
Explanation: V = (4/3)πr³ = (4/3) × (22/7) × 4³ = (4/3) × (22/7) × 64 ≈ 268.8 cm³.
Q8. If the diameter of a circle is 14 cm, its area (π ≈ 22/7) is (a) 154 cm² (b) 308 cm² (c) 616 cm² (d) 77 cm²
Answer: (a)
Explanation: Radius = d/2 = 7 cm. Area = πr² = (22/7) × 7² = 154 cm².
Q9. The lateral surface area of a cone with slant height 10 cm and base radius 6 cm (π ≈ 22/7) is
(a) 188.6 cm² (b) 376.8 cm² (c) 94.3 cm² (d) 471.5 cm² Answer: (a)
Explanation: LSA = πrl = (22/7) × 6 × 10 ≈ 188.6 cm².
Q10. The area of a trapezium whose parallel sides are 8 cm and 12 cm and height 5 cm is
(a) 40 cm² (b) 50 cm² (c) 60 cm² (d) 100 cm² Answer: (b)
Explanation: Area = ½ × (sum of parallel sides) × height = ½ × (8+12) × 5 = 50 cm².
Q11. A rectangular garden 20 m long and 15 m wide is to be fenced. The length of fence required is
(a) 35 m (b) 60 m (c) 70 m (d) 300 m
Answer: (c)
Explanation: Perimeter = 2(20+15) = 70 m.
Q12. The volume of a cuboid with dimensions 4 m × 3 m × 2 m is
(a) 9 m³ (b) 12 m³ (c) 24 m³ (d) 8 m³ Answer: (c)
Explanation: Volume = l × b × h = 4 × 3 × 2 = 24 m³.
Q13. The area of a sector of a circle with radius 10 cm and central angle 60° (π ≈ 22/7) is
(a) 52.38 cm² (b) 104.76 cm² (c) 26.19 cm² (d) 209.52 cm²
Answer: (a)
Explanation: Area = (θ/360)πr² = (60/360) × (22/7) × 10² = (1/6) × (22/7) × 100 ≈ 52.38 cm².
Q14. The curved surface area of a hemisphere of radius 9 cm (π ≈ 22/7) is
(a) 254.34 cm² (b) 508.68 cm² (c) 127.17 cm² (d) 1017.36 cm²
Answer: (b)
Explanation: CSA of hemisphere = 2πr² = 2 × (22/7) × 9² = 2 × (22/7) × 81 ≈ 508.68 cm².
Q15. If the side of an equilateral triangle is 6 cm, its area is
(a) 9√3 cm² (b) 12√3 cm² (c) 6√3 cm² (d) 18√3 cm²
Answer: (a) Explanation: Area = (√3/4)a² = (√3/4) × 6² = (√3/4) × 36 = 9√3 cm².
Q16. The perimeter of a regular hexagon with each side 5 cm is
(a) 20 cm (b) 25 cm (c) 30 cm (d) 35 cm
Answer: (c)
Explanation: Perimeter = 6 × side = 6 × 5 = 30 cm.
Q17. The volume of a right circular cone with radius 3 cm and height 4 cm (π ≈ 22/7) is
(a) 37.71 cm³ (b) 75.43 cm³ (c) 18.85 cm³ (d) 56.57 cm³ Answer: (a)
Explanation: V = (1/3)πr²h = (1/3) × (22/7) × 3² × 4 = (1/3) × (22/7) × 9 × 4 ≈ 37.71 cm³.
Q18. The total surface area of a cube of side 6 cm is
(a) 36 cm² (b) 72 cm² (c) 216 cm² (d) 144 cm²
Answer: (c)
Explanation: TSA = 6a² = 6 × 6² = 6 × 36 = 216 cm².
Q19. A circular pond has a diameter of 14 m. The length of rope needed to go once around the pond (π ≈ 22/7) is (a) 22 m (b) 44 m (c) 88 m (d) 154 m
Answer: (b)
Explanation: Circumference = πd = (22/7) × 14 = 44 m.
Q20. The area of a rhombus with diagonals 10 cm and 8 cm is
(a) 40 cm² (b) 80 cm² (c) 20 cm² (d) 16 cm²
Answer: (a) Explanation: Area = (d₁ × d₂)/2 = (10 × 8)/2 = 40 cm².
Q21. The volume of a sphere whose surface area is 616 cm² (π ≈ 22/7) is (a) 1437.33 cm³ (b) 718.67 cm³ (c) 359.33 cm³ (d) 179.67 cm³
Answer: (b)
Explanation: Surface area = 4πr² → r² = (616)/(4π) = 616/(4 × 22/7) = 616 × 7/(88) = 49 → r = 7 cm. Volume = (4/3)πr³ = (4/3) × (22/7) × 343 ≈ 718.67 cm³.
Q22. The lateral surface area of a cylinder of radius 5 cm and height 12 cm (π ≈ 22/7) is
(a) 376.8 cm² (b) 188.4 cm² (c) 753.6 cm² (d) 94.2 cm²
Answer: (a)
Explanation: LSA = 2πrh = 2 × (22/7) × 5 × 12 = (44/7) × 60 ≈ 376.8 cm².
Q23. The area of a regular pentagon with side 4 cm and apothem 2.75 cm is
(a) 27.5 cm² (b) 55 cm² (c) 13.75 cm² (d) 22 cm²
Answer: (a)
Explanation: Area = (1/2) × perimeter × apothem = 0.5 × (5 × 4) × 2.75 = 0.5 × 20 × 2.75 = 27.5 cm².
Q24. A rectangular plot 50 m long and 30 m wide is to be covered with grass. If 1 m² of grass costs ₹20, the total cost is
(a) ₹30,000 (b) ₹20,000 (c) ₹40,000 (d) ₹50,000
Answer: (a)
Explanation: Area = 50 × 30 = 1500 m². Cost = 1500 × 20 = ₹30,000.
Q25. The volume of a hemisphere of radius 6 cm (π ≈ 22/7) is
(a) 452.16 cm³ (b) 904.32 cm³ (c) 226.08 cm³ (d) 301.44 cm³
Answer: (c)
Explanation: Volume of hemisphere = (2/3)πr³ = (2/3) × (22/7) × 6³ = (2/3) × (22/7) × 216 ≈ 226.08 cm³.
