Class 9 Surface Area of a Cone — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which formula gives the curved surface area of a right circular cone with base radius r and slant height l?
Aπr(l + r)
B2πrl
Cπrl
Dπr²l
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Answer: C) πrl
Curved surface area = πrl. πr(l + r) is the TOTAL surface area (curved part plus the circular base πr²).
2. A joker's cap is a cone of base radius 7 cm and height 24 cm. How much sheet is needed to make one cap? (π = 722)
A704 cm²
B550 cm²
C1232 cm²
D528 cm²
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Answer: B) 550 cm²
l = √(49 + 576) = √625 = 25 cm. The cap has no base, so sheet = CSA = 722 × 7 × 25 = 550 cm². (528 uses h = 24; 704 adds a base that the cap does not have.)
3. A cone's base has area 154 cm² and its slant height is 15 cm. Find its curved surface area. (π = 722)
A2310 cm²
B165 cm²
C330 cm²
D484 cm²
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Answer: C) 330 cm²
πr² = 154 → r² = 49 → r = 7 cm. CSA = 722 × 7 × 15 = 330 cm². (484 cm² is the total surface area.)
4. Which change keeps the curved surface area of a cone the same?
ADouble the radius and halve the slant height
BAdd 2 cm to both
CHalve the radius only
DDouble both radius and slant height
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Answer: A) Double the radius and halve the slant height
CSA = πrl. (2r)(l/2) = rl, so the product is unchanged. All other options change r × l.
5. Fifty hollow traffic cones, each with base diameter 40 cm and height 1 m, are painted on the outside at ₹12 per m². Using π = 3.14 and √1.04 ≈ 1.02, what is the cost?
A₹459.70
B₹768.67
C₹384.34
D₹376.80
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Answer: C) ₹384.34
r = 0.2 m, l = √(0.04 + 1) = √1.04 ≈ 1.02 m. One cone: 3.14 × 0.2 × 1.02 = 0.64056 m². Fifty cones: 32.028 m². Cost = 32.028 × 12 ≈ ₹384.34. (₹376.80 uses h for l; ₹768.67 uses the diameter.)