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Observe the given figure and answer the following questions :[Figure: a solid cone with apex P and centre of the base O; AB is a diameter of the circular base, so A and B are on the base circle; seg PO is drawn to O with a right-angle mark at O, and…

Q.5 (2) Observe the given figure and answer the following questions :

[Figure: a solid cone with apex P and centre of the base O; AB is a diameter of the circular base, so A and B are on the base circle; seg PO is drawn to O with a right-angle mark at O, and PA, PB are the slant edges.]

(i) How many surfaces does a solid cone have ?
(ii) What are the names of slant height and perpendicular height in the given figure ?
(iii) If slant height of solid cone is 10 cm and perpendicular height is 8 cm, then find diameter of base of solid cone ?

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Answer: (i) 2 surfaces; (ii) slant height = PA (or PB) and perpendicular height = PO; (iii) diameter = 12 cm.

(i) A solid cone has two surfaces — one curved (lateral) surface and one flat circular base.

(ii) In the figure the slant height is seg PA (also seg PB) and the perpendicular height is seg PO, the perpendicular from the apex to the centre of the base.

(iii) In right Δ POA, \(r^2 = l^2 - h^2 = 10^2 - 8^2 = 100 - 64 = 36\), so r = 6 cm.

Diameter of the base = 2r = 2 × 6 = 12 cm.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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