Practice Questions
Concept Explanation
A right circular cone has circular base radius r, vertical height h, and slant height l where l² = r² + h². Use π = 22/7.
Formulas
- Volume V = (1/3)πr²h
- CSA = πrl
- TSA = πr(r + l)
Example
r = 7 cm, h = 24 cm: l = 25 cm, V = (1/3) × (22/7) × 49 × 24 = 1232 cu cm.
Common Trap
Do not use h in place of slant height l in CSA formula.
-
Q1 EasyVolume of cone r = 7 cm, h = 9 cm (π = 22/7) is:ExplanationV = (1/3) πr²h = (1/3) × 154 × 9 = 462 cu cm. Hence the answer is 462 cu cm.
-
Q2 EasySlant height of cone r = 7 cm, h = 24 cm is:Explanationl = √(7² + 24²) = √625 = 25 cm. Hence the answer is 25 cm.
-
Q3 EasyIce-cream cone r = 3.5 cm, l = 10 cm (π = 22/7). CSA:ExplanationCSA = πrl = (22/7) × 3.5 × 10 = 110 sq cm. Hence the answer is 110 sq cm.
-
Q4 MediumConical tent r = 7 m, h = 24 m (π = 22/7). Canvas for curved surface (CSA):Explanationl = 25 m, CSA = 550 sq m. Hence the answer is 550 sq m.
-
Q5 MediumCone volume 462 cu cm, r = 7 cm (π = 22/7). Height:Explanationh = 462 × 3 / 154 = 9 cm. Hence the answer is 9 cm.
-
Q6 MediumCone radius doubled, height halved. Volume becomes:ExplanationV ∝ r²h: (2)² × (1/2) = 2 times. Hence the answer is Double.
-
Q7 MediumCSA of cone r = 7 cm, l = 25 cm (π = 22/7) is:ExplanationCSA = πrl = (22/7) × 7 × 25 = 550 sq cm. Hence the answer is 550 sq cm.
-
Q8 MediumCone and cylinder share r = 7 cm, h = 12 cm (π = 22/7). Cone volume is:ExplanationCylinder V = 1848, cone = 1848/3 = 616 cu cm. Hence the answer is 616 cu cm.
-
Q9 MediumCone slant 13 cm, r = 5 cm. Height:Explanationh = √(169 − 25) = 12 cm. Hence the answer is 12 cm.
-
Q10 MediumCone height 12 cm, r = 7 cm (π = 22/7). Volume is:ExplanationV = (1/3) × 154 × 12 = 616 cu cm. Hence the answer is 616 cu cm.
-
Q11 HardCylinder volume equals cone with same r and h (π = 22/7), r = 7, h = 9. Cylinder h for same r:ExplanationCone V = 462. Cylinder needs πr²h = 462, h = 3 cm. Hence the answer is 3 cm.
-
Q12 HardFunnel conical part r = 7 cm, h = 24 cm. Volume (π = 22/7):ExplanationV = (1/3) × 154 × 24 = 1232 cu cm. Hence the answer is 1232 cu cm.
-
Q13 HardTSA of cone r = 7 cm, l = 25 cm (π = 22/7) is:ExplanationTSA = πr(r + l) = (22/7) × 7 × 32 = 704 sq cm. Hence the answer is 704 sq cm.
-
Q14 HardCone filled to half height (similar cones). Fraction of full volume:ExplanationLinear scale 1/2 gives volume scale (1/2)³ = 1/8. Hence the answer is 1/8.
-
DS1 Easy
What is the volume of the cone? (π = 22/7)
Statement IRadius 7 cm and height 9 cm.
Statement IISlant height 25 cm and radius 7 cm.
ExplanationStatement I alone: V = 462 cu cm. Statement II gives l but h still needed unless using l²=r²+h². Answer: A. -
DS2 Easy
What is the curved surface area? (π = 22/7)
Statement Ir = 7 cm, l = 25 cm.
Statement IIr = 7 cm, h = 24 cm.
ExplanationStatement I: CSA = 550 sq cm. Statement II: l = 25, CSA = 550 sq cm. Each alone sufficient. Answer: D.
-
DS3 Medium
What is the slant height of the cone?
Statement IRadius is 7 cm and height is 24 cm.
Statement IIr = 7 cm and CSA is 550 sq cm (π = 22/7).
ExplanationStatement I: l = 25 cm. Statement II: l = CSA/(πr) = 25 cm. Each alone sufficient. Answer: D. -
DS4 Medium
What is the height of the cone?
Statement IVolume is 616 cu cm and radius is 7 cm (π = 22/7).
Statement IISlant height is 25 cm and radius is 7 cm.
ExplanationStatement I: 616 = (1/3) × 154 × h, so h = 12 cm. Statement II: h = √(25² − 7²) = 24 cm. Each alone gives a unique height. Answer: D.