Volume and Surface Area — 24 Aptitude Questions and Answers with Explanations

Volume and Surface Area — Questions and Answers

Volume and Surface Area extends mensuration into three dimensions. The examiner's favourite trick is scaling: doubling the radius of a sphere multiplies the volume by 8, not 2, because volume depends on the cube of the length. Keep the cube, cuboid, cylinder, cone and sphere formulas at your fingertips and the rest is arithmetic.

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Volume and Surface Area— Concepts, Formulas & Shortcuts

Cube: volume = a³, total surface area = 6a², diagonal = a√3.
Cuboid: volume = lbh, TSA = 2(lb + bh + hl), diagonal = √(l² + b² + h²).
Cylinder: volume = πr²h, curved surface = 2πrh, total surface = 2πr(r + h).
Cone: volume = ⅓πr²h, curved surface = πrl where l = √(r² + h²).
Sphere: volume = 4/3 πr³, surface area = 4πr². Hemisphere: volume = ⅔πr³, TSA = 3πr².
Scaling: if every length is multiplied by k, area scales by k² and volume by k³.

Volume and Surface Area Practice Questions with Answers

Attempt each question first, then open the explanation. All 24 questions below are free to read and require no signup.

Q1.The volume of a cube of side 5 cm is:
Easy
- A25 cm³
- B75 cm³
- C125 cm³
- D150 cm³
+Show Answer & Explanation
Answer: C. 125 cm³
Explanation: Volume = a³ = 5³ = 125 cm³.
Volume and Surface Area question 1 of 24
Q2.The total surface area of a cube of side 4 cm is:
Easy
- A16 cm²
- B64 cm²
- C96 cm²
- D128 cm²
+Show Answer & Explanation
Answer: C. 96 cm²
Explanation: TSA = 6a² = 6 × 16 = 96 cm².
Volume and Surface Area question 2 of 24
Q3.The volume of a cylinder of radius 7 cm and height 10 cm (π = 22/7) is:
Moderate
- A440 cm³
- B1,100 cm³
- C1,540 cm³
- D2,200 cm³
+Show Answer & Explanation
Answer: C. 1,540 cm³
Explanation: πr²h = 22/7 × 49 × 10 = 1,540 cm³.
Volume and Surface Area question 3 of 24
Q4.The curved surface area of a cylinder of radius 7 cm and height 10 cm (π = 22/7) is:
Moderate
- A220 cm²
- B440 cm²
- C660 cm²
- D880 cm²
+Show Answer & Explanation
Answer: B. 440 cm²
Explanation: 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².
Volume and Surface Area question 4 of 24
Q5.The volume of a sphere of radius 3 cm is:
Moderate
- A12π cm³
- B27π cm³
- C36π cm³
- D48π cm³
+Show Answer & Explanation
Answer: C. 36π cm³
Explanation: 4/3 πr³ = 4/3 × π × 27 = 36π ≈ 113.1 cm³.
Volume and Surface Area question 5 of 24
Q6.The volume of a cone of radius 3 cm and height 4 cm is:
Moderate
- A9π cm³
- B12π cm³
- C24π cm³
- D36π cm³
+Show Answer & Explanation
Answer: B. 12π cm³
Explanation: ⅓πr²h = ⅓ × π × 9 × 4 = 12π ≈ 37.7 cm³.
Volume and Surface Area question 6 of 24
Q7.The length of the diagonal of a cube of side 4 cm is:
Moderate
- A4 cm
- B4√2 cm
- C4√3 cm
- D8 cm
+Show Answer & Explanation
Answer: C. 4√3 cm
Explanation: Diagonal of a cube = a√3 = 4√3 ≈ 6.93 cm.
Volume and Surface Area question 7 of 24
Q8.If the radius of a sphere is doubled, its volume becomes:
Moderate
- A2 times
- B4 times
- C6 times
- D8 times
+Show Answer & Explanation
Answer: D. 8 times
Explanation: Volume varies as r³, so doubling the radius multiplies the volume by 2³ = 8.
Volume and Surface Area question 8 of 24
Q9.The volume of a cuboid 8 cm × 5 cm × 3 cm is:
Easy
- A100 cm³
- B110 cm³
- C120 cm³
- D150 cm³
+Show Answer & Explanation
Answer: C. 120 cm³
Explanation: Volume = lbh = 8 × 5 × 3 = 120 cm³.
Volume and Surface Area question 9 of 24
Q10.The surface area of a sphere of radius 7 cm (π = 22/7) is:
Moderate
- A154 cm²
- B308 cm²
- C616 cm²
- D1,232 cm²
+Show Answer & Explanation
Answer: C. 616 cm²
Explanation: 4πr² = 4 × 22/7 × 49 = 616 cm².
Volume and Surface Area question 10 of 24
Q11.If the side of a cube is doubled, its total surface area becomes:
Moderate
- A2 times
- B4 times
- C6 times
- D8 times
+Show Answer & Explanation
Answer: B. 4 times
Explanation: Surface area varies as the square of the side, so doubling gives 2² = 4 times.
Volume and Surface Area question 11 of 24
Q12.The volume of a cylinder of radius 3.5 cm and height 8 cm (π = 22/7) is:
Moderate
- A154 cm³
- B231 cm³
- C308 cm³
- D352 cm³
+Show Answer & Explanation
Answer: C. 308 cm³
Explanation: πr²h = 22/7 × 12.25 × 8 = 308 cm³.
Volume and Surface Area question 12 of 24
Q13.The total surface area of a cuboid 5 cm × 4 cm × 3 cm is:
Moderate
- A47 cm²
- B60 cm²
- C94 cm²
- D120 cm²
+Show Answer & Explanation
Answer: C. 94 cm²
Explanation: 2(lb + bh + hl) = 2(20 + 12 + 15) = 2 × 47 = 94 cm².
Volume and Surface Area question 13 of 24
Q14.The slant height of a cone of radius 3 cm and height 4 cm is:
Easy
- A5 cm
- B6 cm
- C7 cm
- D12 cm
+Show Answer & Explanation
Answer: A. 5 cm
Explanation: l = √(r² + h²) = √(9 + 16) = √25 = 5 cm.
Volume and Surface Area question 14 of 24
Q15.The volume of a hemisphere of radius 3 cm is:
Moderate
- A9π cm³
- B18π cm³
- C27π cm³
- D36π cm³
+Show Answer & Explanation
Answer: B. 18π cm³
Explanation: ⅔πr³ = ⅔ × π × 27 = 18π cm³.
Volume and Surface Area question 15 of 24
Q16.A cube of side 6 cm is melted and recast into cubes of side 2 cm. The number of small cubes formed is:
Moderate
- A9
- B18
- C27
- D36
+Show Answer & Explanation
Answer: C. 27
Explanation: 216/8 = 27 small cubes.
Volume and Surface Area question 16 of 24
Q17.The volume of a cube of side 3 cm is:
Easy
- A9 cm³
- B18 cm³
- C27 cm³
- D54 cm³
+Show Answer & Explanation
Answer: C. 27 cm³
Explanation: Volume of a cube = side³ = 3 × 3 × 3 = 27 cm³.
Volume and Surface Area question 17 of 24
Q18.The volume of a cuboid 10 cm × 6 cm × 4 cm is:
Easy
- A120 cm³
- B180 cm³
- C200 cm³
- D240 cm³
+Show Answer & Explanation
Answer: D. 240 cm³
Explanation: 10 × 6 × 4 = 240 cm³.
Volume and Surface Area question 18 of 24
Q19.The total surface area of a cube of side 5 cm is:
Easy
- A100 cm²
- B125 cm²
- C150 cm²
- D175 cm²
+Show Answer & Explanation
Answer: C. 150 cm²
Explanation: 6a² = 6 × 25 = 150 cm².
Volume and Surface Area question 19 of 24
Q20.If the edge of a cube is 6 cm, its volume is:
Easy
- A36 cm³
- B108 cm³
- C216 cm³
- D252 cm³
+Show Answer & Explanation
Answer: C. 216 cm³
Explanation: Volume of a cube = edge³ = 6 × 6 × 6 = 216 cm³.
Volume and Surface Area question 20 of 24
Q21.The curved surface area of a cone with radius 7 cm and slant height 10 cm (π = 22/7) is:
Moderate
- A154 cm²
- B220 cm²
- C308 cm²
- D440 cm²
+Show Answer & Explanation
Answer: B. 220 cm²
Explanation: πrl = 22/7 × 7 × 10 = 220 cm².
Volume and Surface Area question 21 of 24
Q22.The volume of a cylinder of radius 7 cm and height 5 cm (π = 22/7) is:
Moderate
- A550 cm³
- B660 cm³
- C770 cm³
- D880 cm³
+Show Answer & Explanation
Answer: C. 770 cm³
Explanation: πr²h = 22/7 × 49 × 5 = 770 cm³.
Volume and Surface Area question 22 of 24
Q23.A cube of side 4 cm is cut into 1 cm cubes. The number of small cubes is:
Moderate
- A16
- B32
- C48
- D64
+Show Answer & Explanation
Answer: D. 64
Explanation: 64/1 = 64 small cubes.
Volume and Surface Area question 23 of 24
Q24.The surface area of a sphere of radius 3.5 cm (π = 22/7) is:
Moderate
- A77 cm²
- B154 cm²
- C231 cm²
- D308 cm²
+Show Answer & Explanation
Answer: B. 154 cm²
Explanation: 4πr² = 4 × 22/7 × 12.25 = 154 cm².
Volume and Surface Area question 24 of 24

Volume and Surface Area — Frequently Asked Questions

If the radius of a sphere is doubled, what happens to its volume?+

It becomes 8 times as large, because volume varies as r³ and 2³ = 8. The surface area, varying as r², becomes 4 times as large.

What is the difference between curved and total surface area?+

Curved surface area covers only the lateral surface. Total surface area adds the flat ends — both circles for a cylinder, the single base circle for a cone.

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