Practice Questions
Concept Explanation
A right circular cone has circular base radius r, vertical height h, and slant height l = √(r² + h²).
Key Formulas
- Volume = ⅓ πr²h
- Curved surface area = πrl
- Total surface area = πr(r + l)
Example
r = 7 cm, h = 12 cm, π = 22/7: V = 616 cu cm.
Common Trap
Volume uses height h, not slant height l.
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Q1 Easy
Cone r = 7 cm, h = 12 cm, π = 22/7. Volume is:
ExplanationV = 1/3 × 22/7 × 49 × 12 = 616 cu cm. -
Q2 Medium
Cone r = 7 cm, l = 10 cm, π = 22/7. CSA is:
ExplanationCSA = 22/7 × 7 × 10 = 220 sq cm. -
Q3 Easy
Cone r = 6 cm, h = 8 cm. Slant height is:
Explanationl = √(36 + 64) = 10 cm. -
Q4 Medium
Cone r = 6 cm, h = 8 cm, π = 3.14. Volume is:
ExplanationV = 1/3 × 3.14 × 36 × 8 = 301.44 cu cm. -
Q5 Easy
Cone r = 7 cm, h = 3 cm, π = 22/7. Volume is:
ExplanationV = 1/3 × 22/7 × 49 × 3 = 154 cu cm. -
Q6 Medium
Cone r = 7 cm, l = 25 cm, π = 22/7. CSA is:
ExplanationCSA = 22/7 × 7 × 25 = 550 sq cm. -
Q7 Medium
Cone r = 7 cm, l = 10 cm, π = 22/7. TSA is:
ExplanationTSA = 22/7 × 7 × (7 + 10) = 374 sq cm.
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Q8 Hard
Cone volume 616 cu cm, r = 7 cm, π = 22/7. Height is:
Explanationh = 616 × 3 / (22/7 × 49) = 12 cm. -
Q9 Hard
Cone r = 14 cm, h = 9 cm, π = 22/7. Volume is:
ExplanationV = 1/3 × 22/7 × 196 × 9 = 1848 cu cm. -
Q10 Medium
Cone r = 8 cm, h = 15 cm. Slant height is:
Explanationl = √(64 + 225) = 17 cm. -
Q11 Hard
Cone r = 10 cm, h = 12 cm, π = 3.14. Volume is:
ExplanationV = 1/3 × 3.14 × 100 × 12 = 1256 cu cm. -
Q12 Easy
Same base radius and height for cone and cylinder (π = 22/7, r = 7 cm, h = 12 cm). Cone volume is what fraction of cylinder volume?
ExplanationCone volume is one-third of a cylinder with the same base and height. -
Q13 Hard
Cost of painting CSA of cone (r = 7 cm, l = 10 cm, π = 22/7) at Rs. 5 per sq cm is:
ExplanationCSA = 220 sq cm. Cost = 220 × 5 = Rs. 1100. -
Q14 Easy
If cone height doubles and radius stays same, volume becomes:
ExplanationV ∝ h; doubling h doubles volume.
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DS1 Easy
What is the volume of the cone? (π = 22/7)
Statement IRadius is 7 cm.
Statement IIHeight is 12 cm.
ExplanationNeed both: volume = 616 cu cm. -
DS2 Easy
What is the slant height of the cone?
Statement IRadius is 6 cm.
Statement IIHeight is 8 cm.
ExplanationNeed both: l = 10 cm.
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DS3 Medium
What is the CSA? (π = 22/7)
Statement IRadius is 7 cm.
Statement IISlant height is 10 cm.
ExplanationNeed both: CSA = 220 sq cm. -
DS4 Hard
What is the volume? (π = 22/7)
Statement IRadius is 7 cm and height is 3 cm.
Statement IIVolume is one-third of a cylinder with same r and h.
ExplanationStatement I alone gives volume = 154 cu cm.