51 Volume & Surface Area aptitude questions and answers that are challenging and are designed to give you overall practice. In the answer, we have added a short description and formulas for solving the questions. Hope you will have a great experience and a lot of learning.
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51 Volume & Surface Area Aptitude Questions and Answers (Solved MCQs)
Question 1. The edge of a cube is 7 cm. Its total surface area is:
a) 196 cm²
b) 245 cm²
c) 294 cm²
d) 343 cm²
Answer:
c) 294 cm² — TSA of cube = 6a² = 6 × 7².
Question 2. A cuboid has length 10 cm, breadth 8 cm and height 6 cm. Its volume is:
a) 240 cm³
b) 360 cm³
c) 480 cm³
d) 600 cm³
Answer:
c) 480 cm³ — Volume = l × b × h = 10 × 8 × 6.
Question 3. A cylinder has radius 7 cm and height 10 cm. Its volume is: (Take π = 22/7)
a) 1440 cm³
b) 1540 cm³
c) 1640 cm³
d) 1760 cm³
Answer:
b) 1540 cm³ — V = πr²h = (22/7) × 7² × 10.
Question 4. A cylinder has radius 7 cm and height 10 cm. Its curved surface area is: (Take π = 22/7)
a) 308 cm²
b) 352 cm²
c) 440 cm²
d) 484 cm²
Answer:
c) 440 cm² — CSA = 2πrh = 2 × (22/7) × 7 × 10.
Question 5. The surface area of a sphere of radius 7 cm is: (Take π = 22/7)
a) 308 cm²
b) 616 cm²
c) 770 cm²
d) 924 cm²
Answer:
b) 616 cm² — SA = 4πr² = 4 × (22/7) × 7².
Question 6. The total surface area of a hemisphere of radius 7 cm is: (Take π = 22/7)
a) 308 cm²
b) 462 cm²
c) 616 cm²
d) 770 cm²
Answer:
b) 462 cm² — TSA(hemisphere) = 3πr².
Question 7. A cone has radius 7 cm and height 24 cm. Its curved surface area is: (Take π = 22/7)
a) 484 cm²
b) 550 cm²
c) 616 cm²
d) 704 cm²
Answer:
b) 550 cm² — l = √(7² + 24²) = 25; CSA = πrl = (22/7) × 7 × 25.
Question 8. A cone has radius 7 cm and height 24 cm. Its total surface area is: (Take π = 22/7)
a) 616 cm²
b) 650 cm²
c) 704 cm²
d) 770 cm²
Answer:
c) 704 cm² — TSA = πr(l + r) = (22/7) × 7 × (25 + 7).
Question 9. The volume of a cube is 512 cm³. The edge of the cube is:
a) 6 cm
b) 7 cm
c) 8 cm
d) 9 cm
Answer:
c) 8 cm — a³ = 512 ⇒ a = 8.
Question 10. A cuboid is 12 cm long, 9 cm broad, and 8 cm high. Its total surface area is:
a) 600 cm²
b) 624 cm²
c) 648 cm²
d) 672 cm²
Answer:
b) 624 cm² — TSA = 2(lb + bh + hl) = 2(108 + 72 + 96).
Question 11. The radius of a sphere is increased from 5 cm to 10 cm. Its surface area becomes how many times?
a) 2 times
b) 3 times
c) 4 times
d) 8 times
Answer:
c) 4 times — SA ∝ r²; (10/5)² = 4.
Question 12. The edge of a cube is doubled. Its volume becomes:
a) 2 times
b) 4 times
c) 6 times
d) 8 times
Answer:
d) 8 times — Volume ∝ a³; (2)³ = 8.
Question 13. A cylinder has diameter 14 cm and height 20 cm. Its curved surface area is: (Take π = 22/7)
a) 616 cm²
b) 704 cm²
c) 880 cm²
d) 968 cm²
Answer:
c) 880 cm²
Question 14. The volume of a cylinder is 3080 cm³. If radius = 7 cm, its height is: (Take π = 22/7)
a) 15 cm
b) 18 cm
c) 20 cm
d) 22 cm
Answer:
c) 20 cm — 3080 = (22/7) × 49 × h = 154 × h.
Question 15. A cone has radius 3 cm and slant height 5 cm. Its curved surface area is: (Take π = 3.14)
a) 37.68 cm²
b) 47.10 cm²
c) 54.30 cm²
d) 62.80 cm²
Answer:
b) 47.10 cm² — CSA = πrl = 3.14 × 3 × 5.
Question 16. The total surface area of a cube is 486 cm². Its edge is:
a) 7 cm
b) 8 cm
c) 9 cm
d) 10 cm
Answer:
c) 9 cm — 6a² = 486 ⇒ a² = 81.
Question 17. A hemisphere of radius 7 cm has volume: (Take π = 22/7)
a) 450 cm³
b) 539 cm³
c) 718.66 cm³
d) 1078 cm³
Answer:
c) 718.66 cm³.
Question 1. A solid cuboid 10 cm × 8 cm × 6 cm is melted and recast into cubes of edge 2 cm. Number of cubes formed is:
a) 480
b) 240
c) 120
d) 60
Answer:
c) 120 — Total volume = 480; each cube volume = 8; 480 ÷ 8.
Question 2. A solid sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm. Number of small spheres is:
a) 9
b) 18
c) 27
d) 36
Answer:
c) 27 — Number = (6³)/(2³) = 216/8.
Question 3. A cylinder of radius 7 cm and height 10 cm is melted to form a cone of radius 7 cm. Height of the cone is: (Take π = 22/7)
a) 20 cm
b) 25 cm
c) 30 cm
d) 35 cm
Answer:
c) 30 cm — πr²(10) = (1/3)πr²H ⇒ H = 30.
Question 4. A cone of radius 6 cm and height 8 cm is melted to form a sphere. The radius of the sphere is closest to:
a) 3.0 cm
b) 3.5 cm
c) 4.2 cm
d) 5.0 cm
Answer:
c) 4.2 cm — Volume conserved: (1/3)π×6²×8 = (4/3)πR³ ⇒ 96 = (4/3)R³ ⇒ R³ = 72 ⇒ R ≈ 4.16.
Question 5. A cylindrical pipe has inner radius 4 cm, outer radius 5 cm, and length 20 cm. Volume of metal used is: (Take π = 3.14)
a) 565.2 cm³
b) 565.5 cm³
c) 565.8 cm³
d) 566.0 cm³
Answer:
a) 565.2 cm³ — V = πh(R² − r²) = 3.14 × 20 × (25 − 16).
Question 6. A cube of edge 10 cm is painted on all faces and cut into cubes of edge 2 cm. Number of small cubes with exactly one face painted is:
a) 96
b) 72
c) 54
d) 48
Answer:
b) 72 — n = 10/2 = 5; one-face painted = 6(n−2)² = 6×3².
Question 7. A cube of edge 12 cm is painted on all faces and cut into cubes of edge 3 cm. Number of cubes with no face painted is:
a) 0
b) 1
c) 8
d) 16
Answer:
c) 8 — n = 12/3 = 4; none painted = (n−2)³ = 2³.
Question 8. A rectangular tank (open at top) is 8 m long, 6 m wide and 3 m deep. Area of sheet required to make it is:
a) 156 m²
b) 168 m²
c) 180 m²
d) 192 m²
Answer:
b) 168 m² — Open tank area = base + 4 walls = lw + 2lh + 2wh = 48 + 48 + 36.
Question 9. A cylindrical water tank has radius 3 m and height 7 m. Capacity in liters is: (Take π = 22/7)
a) 138,600 L
b) 176,000 L
c) 198,000 L
d) 207,900 L
Answer:
c) 198,000 L.
Question 10. The cost of painting the curved surface of a cylinder (r = 7 cm, h = 20 cm) at ₹0.50 per cm² is:
a) ₹220
b) ₹440
c) ₹484
d) ₹560
Answer:
b) ₹440 — CSA = 2πrh = 2 × (22/7) × 7 × 20 = 880; cost = 880 × 0.50.
Question 11. A solid cube of edge 6 cm is hollowed out to form a cubical box with thickness 1 cm on all sides. Volume of the hollow part is:
a) 64 cm³
b) 72 cm³
c) 80 cm³
d) 96 cm³
Answer:
a) 64 cm³ — Inner edge = 6 − 2×1 = 4; hollow volume = 4³.
Question 12. A hemispherical bowl of radius 7 cm is filled with water and poured into a cylindrical jar of radius 3.5 cm. Height of water in the jar is: (Take π = 22/7)
a) 7 cm
b) 9 cm
c) 10.67 cm
d) 14 cm
Answer:
c) 10.67 cm — (2/3)π×7³ = π×(3.5)²×h ⇒ h = (2/3)×343 / 12.25.
Question 13. A cone has base radius 6 cm and height 8 cm. It is filled with water and poured into a cylinder of radius 3 cm. Height of water in cylinder is:
a) 8 cm
b) 10 cm
c) 12 cm
d) 16 cm
Answer:
c) 12 cm — (1/3)π×6²×8 = π×3²×h ⇒ 96 = 9h.
Question 14. A cuboid of dimensions 15 cm × 10 cm × 6 cm is dipped in paint. Total painted area is:
a) 600 cm²
b) 660 cm²
c) 720 cm²
d) 780 cm²
Answer:
c) 720 cm² — TSA = 2(lb + bh + hl) = 2(150 + 60 + 90).
Question 15. A sphere and a cube have equal volumes. If the edge of the cube is 6 cm, radius of the sphere is closest to: (Take π = 3.14)
a) 3.2 cm
b) 3.7 cm
c) 4.1 cm
d) 4.8 cm
Answer:
b) 3.7 cm — 6³ = (4/3)πr³ ⇒ r³ = 216×3/(4π) ≈ 51.6 ⇒ r ≈ 3.7.
Question 16. A cylindrical log has radius 14 cm and length 1 m. Volume of the log is: (Take π = 22/7)
a) 30,800 cm³
b) 61,600 cm³
c) 92,400 cm³
d) 123,200 cm³
Answer:
b) 61,600 cm³ — h = 100 cm; V = πr²h = (22/7) × 14² × 100.
Question 1. The radius of a cylinder is tripled and height is doubled. The volume becomes:
a) 6 times
b) 9 times
c) 12 times
d) 18 times
Answer:
d) 18 times — V ∝ r²h ⇒ (3²)×2 = 18.
Question 2. The edge of a cube is increased by 20%. The total surface area increases by:
a) 20%
b) 40%
c) 44%
d) 72%
Answer:
c) 44% — TSA ∝ a² ⇒ (1.2)² = 1.44.
Question 3. The edge of a cube is decreased by 10%. The volume decreases by:
a) 10%
b) 19%
c) 27.1%
d) 30%
Answer:
c) 27.1% — Volume ∝ a³ ⇒ (0.9)³ = 0.729.
Question 4. A cube is cut into 125 equal smaller cubes. The ratio of total surface area of all small cubes to that of the original cube is:
a) 5:1
b) 10:1
c) 25:1
d) 125:1
Answer:
a) 5:1 — n = 5; TSA scales by n for equal partition: ratio = n = 5.
Question 5. A cuboid has volume 720 cm³. If l = 12 cm and b = 10 cm, then height is:
a) 4 cm
b) 5 cm
c) 6 cm
d) 8 cm
Answer:
c) 6 cm — h = 720 ÷ (12 × 10).
Question 6. A right circular cone has radius 6 cm and slant height 10 cm. Its height is:
a) 6 cm
b) 8 cm
c) 10 cm
d) 12 cm
Answer:
b) 8 cm — h = √(l² − r²) = √(100 − 36).
Question 7. A sphere has volume 288π cm³. Its radius is:
a) 3 cm
b) 4 cm
c) 6 cm
d) 8 cm
Answer:
c) 6 cm — (4/3)πr³ = 288π ⇒ r³ = 216.
Question 8. A cylinder has volume 616 cm³. If r = 7 cm, height is: (Take π = 22/7)
a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm
Answer:
b) 4 cm — V = (22/7)×49×h = 154h.
Question 9. A hemispherical solid has volume 324π cm³. Its radius is:
a) 6 cm
b) 7 cm
c) 8 cm
d) 9 cm
Answer:
c) 8 cm — (2/3)πr³ = 324π ⇒ r³ = 486 ⇒ r ≈ 7.86 (closest 8).
Question 10. A cube of edge 9 cm is painted on all faces and cut into cubes of edge 1 cm. Number of cubes with exactly three faces painted is:
a) 6
b) 8
c) 12
d) 27
Answer:
b) 8 — Only the 8 corner cubes have 3 faces painted.
Question 11. A cube is painted and cut into n × n × n smaller cubes. Number of cubes with exactly two faces painted is:
a) 12(n − 2)
b) 6(n − 2)²
c) 8(n − 2)³
d) 12(n − 1)
Answer:
a) 12(n − 2) — Edge cubes excluding corners.
Question 12. A cylindrical tank has diameter 14 m and height 10 m. Its total inner surface area (including base) is: (Take π = 22/7)
a) 528 m²
b) 616 m²
c) 704 m²
d) 836 m²
Answer:
d) 836 m² — Inner area = CSA + base = 2πrh + πr² = 2×(22/7)×7×10 + (22/7)×49 = 440 + 154.
Question 13. DATA SUFFICIENCY: Find the volume of a cuboid.
I. Its length is 12 cm and breadth is 8 cm.
II. Its total surface area is 416 cm².
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Even together not sufficient
Answer:
c) Both together sufficient, neither alone
Question 14. DATA SUFFICIENCY: Find the radius of a sphere.
I. Its surface area is 616 cm².
II. Take π = 22/7.
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Even together not sufficient
Answer:
c) Both together sufficient, neither alone — Need π value to compute r from 4πr².
Question 15. A cube and a cuboid have equal total surface areas. Cube edge = 6 cm. Cuboid dimensions are 8 cm × 4 cm × h cm. The value of h is:
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer:
b) 5 cm — TSA cube = 6×6²=216; TSA cuboid = 2(32 + 4h + 8h)=64+24h; set 64+24h=216.
Question 16. A cylinder and a cone have the same base radius 7 cm and the same height 12 cm. The ratio of their volumes is:
a) 1:2
b) 2:1
c) 3:1
d) 1:3
Answer:
c) 3:1 — Cylinder volume is 3 times cone volume for same r and h.
Question 17. A solid cylinder of radius 6 cm and height 9 cm is melted to form 8 identical cones, each of height 9 cm. The radius of each cone is:
a) 3 cm
b) 3.5 cm
c) (3√6)/2 cm
d) 4 cm
Answer:
c) (3√6)/2 cm — Volume conserved: π×6²×9 = 8×(1/3)π×r²×9 ⇒ 36 = 8r²/3 ⇒ r² = 13.5 = 27/2 ⇒ r = (3√6)/2.
Question 18. A sphere of radius 3 cm is placed inside a cylinder of radius 3 cm. Minimum height of the cylinder to fully contain the sphere is:
a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm
Answer:
d) 6 cm — Height must be the diameter = 2r.
