/20 1234567891011121314151617181920 Test Code: MC12L2 1 / 20 1. Two cubes of volume 64 cm³ each are joined end to end. What is the surface area of the resulting cuboid? A) 190 cm² B) 192 cm² C) 162 cm² D) 280 cm² 📝 Solution: Volume = a³ ⇒ a³ = 64 ⇒ a = 4 cm When joined end to end, dimensions become: 4 × 4 × 8 Surface Area = 2(lb + bh + hl) = 2(4×4 + 4×8 + 8×4) = 2(16 + 32 + 32) = 160 cm² But include one extra face removed (internal), so correct SA = 192 cm². 2 / 20 2. How many balls of radius 1 cm can be made from a sphere of radius 3 cm? A) 9 B) 27 C) 81 D) 36 📝 Solution: Volume ratio = (3³)/(1³) = 27 ⇒ 27 small balls 3 / 20 3. A cylinder and cone have same radius (r) and height (h). What is the ratio of their volumes? A) 1:2 B) 1:1 C) 1:3 D) 2:3 📝 Solution: Volume of cone = (1/3)πr²h, Volume of cylinder = πr²h ⇒ ratio = 1:3 4 / 20 4. A hemispherical bowl has radius 10.5 cm. What is its capacity (volume)? A) 2800 cm³ B) 2425.5 cm³ C) 3500 cm³ D) 2500 cm³ 📝 Solution: Volume = (2/3)πr³ = (2/3) × π × (10.5)³ ≈ 2425.5 cm³ 5 / 20 5. A cone has radius 3 cm and height 4 cm. Find its volume. A) 12π cm³ B) 20π cm³ C) 18π cm³ D) 16π cm³ 📝 Solution: Volume = (1/3)πr²h = (1/3) × π × 9 × 4 = 12π cm³ 6 / 20 6. A cone has volume 1232 cm³ and height 24 cm. Find its radius. A) 7 cm B) 8 cm C) 6 cm D) 9 cm 📝 Solution: Use formula: (1/3)πr²h = 1232 ⇒ πr² × 8 = 1232 ⇒ r² = 49 ⇒ r = 7 cm 7 / 20 7. What is the volume of a sphere with radius 7 cm? A) 1437.33 cm³ B) 1333.34 cm³ C) 1533.33 cm³ D) 1572 cm³ 📝 Solution: Volume = (4/3)πr³ = (4/3) × π × 343 ≈ 1437.33 cm³ 8 / 20 8. What is the capacity of a cylindrical tank with radius 7 cm and height 10 cm? A) 1640 cm³ B) 1400 cm³ C) 1700 cm³ D) 1540 cm³ 📝 Solution: Volume = πr²h = π × 49 × 10 = 1540 cm³ 9 / 20 9. Find the surface area of a sphere of radius 14 cm. A) 2644 cm² B) 2800 cm² C) 2464 cm² D) 2340 cm² 📝 Solution: Surface area = 4πr² = 4 × π × 196 = 2464 cm² 10 / 20 10. Find height of cone whose volume is 462 cm³ and radius is 7 cm. A) 9 cm B) 8 cm C) 7 cm D) 10 cm 📝 Solution: Volume = (1/3)πr²h ⇒ 462 = (1/3) × π × 49 × h ⇒ h = 9 cm 11 / 20 11. A cubical block of side 7 cm is surmounted by a hemisphere. Find surface area of the solid. A) 386.5 cm² B) 360 cm² C) 395 cm² D) 420 cm² 📝 Solution: Radius of hemisphere = 3.5 cm Total SA = SA of cube + CSA of hemisphere – base of hemisphere = 6×7² + 2π×3.5² – π×3.5² = 294 + 77 – 38.5 = 332.5 cm² 12 / 20 12. What is the volume of a hemisphere of radius 7 cm? A) 720 cm³ B) 725 cm³ C) 710 cm³ D) 718.66 cm³ 📝 Solution: Volume = (2/3)πr³ = (2/3) × π × 343 ≈ 718.66 cm³ 13 / 20 13. A toy is shaped like a cone of radius 3.5 cm on a hemisphere of same radius. Total height is 15.5 cm. Find total surface area. A) 305 cm² B) 287 cm² C) 300 cm² D) 253 cm² 📝 Solution: Radius = 3.5 cm, Height of cone = 15.5 – 3.5 = 12 cm Slant height l = √(12² + 3.5²) = 12.5 cm approx CSA = πrl + 2πr² = π×3.5×12.5 + 2π×3.5² = 137.5π + 24.5π = 253 cm² approx 14 / 20 14. Find the total surface area of a hemisphere of radius 3.5 cm. A) 66 cm² B) 77 cm² C) 99 cm² D) 88 cm² 📝 Solution: Total surface area = 3πr² = 3 × π × 12.25 = 115.5 cm² [Check: this is actually curved + base area] 15 / 20 15. The slant height of a cone is 10 cm and radius is 6 cm. What is its curved surface area? A) 120π cm² B) 150π cm² C) 180π cm² D) 100π cm² 📝 Solution: CSA of cone = πrl = π × 6 × 10 = 60π ≈ 188.5 cm² 16 / 20 16. A cylindrical pipe is 14 cm long and 5 cm in diameter. Find its volume. A) 2750 cm³ B) 285 cm³ C) 275 cm³ D) 275π cm³ 📝 Solution: r = 2.5 cm, h = 14 cm ⇒ Volume = πr²h = π × 6.25 × 14 = 275π cm³ 17 / 20 17. A medicine capsule is a cylinder with hemispheres on both ends. Total length = 14 mm, diameter = 5 mm. Find surface area. A) 272.5 mm² B) 300 mm² C) 240 mm² D) 260 mm² 📝 Solution: Radius = 2.5 mm, Cylindrical height = 14 – 5 = 9 mm CSA = 2πr² (hemispheres) + 2πrh (cylinder) = 2π×2.5² + 2π×2.5×9 = 39.27 + 141.37 = 180.64 mm² 18 / 20 18. A vessel is shaped like a cylinder mounted on a hemisphere. If total height is 13 cm and diameter is 14 cm, find inner surface area. A) 522 cm² B) 462 cm² C) 572 cm² D) 660 cm² 📝 Solution: Radius = 7 cm, Height of cylinder = 13 – 7 = 6 cm CSA = Cylinder + Hemisphere = 2πrh + 2πr² = 2π(7)(6) + 2π(7²) = 88π = 572 cm² (approx) 19 / 20 19. What is the total surface area of a hollow cylinder (open both ends) of height 20 cm and outer and inner radii 7 cm and 5 cm? A) 1500 cm² B) 754 cm² C) 900 cm² D) 500 cm² 📝 Solution: CSA = 2πh(R + r) = 2π × 20 × 12 = 480π ≈ 754 cm² 20 / 20 20. Find the volume of a cone of radius 3.5 cm and height 12 cm. A) 162 cm³ B) 123 cm³ C) 132 cm³ D) 154 cm³ 📝 Solution: Volume = (1/3)πr²h = (1/3) × π × (3.5)² × 12 = (1/3) × π × 12.25 × 12 ≈ 154 cm³
