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Surface Areas and Volumes — Class 9 CBSE Mathematics MCQs with Solutions
Free Class 9 CBSE Mathematics Surface Areas and Volumes MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — easy
Curved Surface Area (CSA) of a right circular cone with radius r and slant height l is:
A. 2πrl
B. πrl ✓ Correct
C. πr(r + l)
D. ⅓ πr²h
Solution: CSA of cone = πrl.
Q2 — easy
Total Surface Area (TSA) of a cone with radius r and slant height l is:
A. πrl
B. πr(r + l) ✓ Correct
C. 2πr(r + h)
D. πr²l
Solution: TSA = CSA + Base Area = πrl + πr² = πr(r + l).
Q3 — easy
Slant height l, radius r, and height h of a right circular cone are related by:
A. l = r + h
B. l = √(r² + h²) ✓ Correct
C. l = r² + h²
D. h = √(r² + l²)
Solution: Pythagorean relation in cone: l² = r² + h² → l = √(r² + h²).
Q4 — easy
Surface Area (S) of a sphere of radius r is:
A. 2πr²
B. 3πr²
C. 4πr² ✓ Correct
D. 4/3 πr²
Solution: Sphere surface area = 4πr².
Q5 — easy
Curved Surface Area (CSA) of a hemisphere of radius r is:
A. 2πr² ✓ Correct
B. 3πr²
C. 4πr²
D. πr²
Solution: Hemisphere CSA = ½ (4πr²) = 2πr².
Q6 — easy
Total Surface Area (TSA) of a SOLID hemisphere of radius r is:
A. 2πr²
B. 3πr² ✓ Correct
C. 4πr²
D. πr²
Solution: Solid hemisphere TSA = CSA + Flat base = 2πr² + πr² = 3πr².
Q7 — easy
Volume (V) of a sphere of radius r is:
A. 4πr³
B. 4/3 πr³ ✓ Correct
C. ⅔ πr³
D. ⅓ πr³
Solution: Volume of sphere = 4/3 πr³.
Q8 — easy
Volume (V) of a hemisphere of radius r is:
A. 4/3 πr³
B. ⅔ πr³ ✓ Correct
C. ⅓ πr³
D. 3πr³
Solution: Volume of hemisphere = ⅔ πr³.
Q9 — easy
Find slant height of a cone having radius 3 cm and height 4 cm:
A. 5 cm ✓ Correct
B. 7 cm
C. 25 cm
D. 6 cm
Solution: l = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Q10 — easy
If radius of a sphere is doubled (2r), its surface area becomes:
A. 2 times
B. 4 times ✓ Correct
C. 8 times
D. 16 times
Solution: Surface area ∝ r², so (2r)² = 4r² (4 times).
Q11 — easy
If radius of a sphere is doubled (2r), its volume becomes:
A. 2 times
B. 4 times
C. 8 times ✓ Correct
D. 16 times
Solution: Volume ∝ r³, so (2r)³ = 8r³ (8 times).
Q12 — easy
Ratio of volume of a cylinder to volume of a cone of SAME radius and height is:
A. 1 : 3
B. 3 : 1 ✓ Correct
C. 1 : 1
D. 2 : 3
Solution: V_cylinder / V_cone = πr²h / (⅓πr²h) = 3 / 1 = 3 : 1.
Q13 — medium
Volume (V) of a right circular cone with radius r and height h is:
A. πr²h
B. ⅓ πr²h ✓ Correct
C. ⅔ πr²h
D. 4/3 πr³
Solution: Volume of cone = ⅓ × Volume of cylinder = ⅓ πr²h.
Q14 — medium
Find volume of a cone with radius 6 cm and height 7 cm: (take π = 22/7)
A. 264 cm³ ✓ Correct
B. 132 cm³
C. 792 cm³
D. 528 cm³
Solution: V = ⅓ × (22/7) × 6 × 6 × 7 = ⅓ × 22 × 36 = 264 cm³.
Q15 — medium
Find surface area of a sphere of radius 7 cm: (take π = 22/7)
A. 154 cm²
B. 308 cm²
C. 616 cm² ✓ Correct
D. 1386 cm²
Solution: S = 4 × (22/7) × 7 × 7 = 4 × 154 = 616 cm².