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Question

The total surface area of a right circular cone of slant height 13 cm is 90π cm2. Calculate :
(i) its radius in cm,
(ii) its volume in cm3, in terms of π.

[4 MARKS]


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Solution

Concept: 1 Mark
Application: 3 Marks

Given : slant height , l=13cm.

Let, radius = r cm and height = h cm.

(i) Total surface area = πr(l+r)=[πr(13+r)] cm2.

πr(13+r)=90π

r2+13r90=0

(r+18)(r5)=0

r=5 [Neglecting r=-18, as radius cannot be negative]

Radius of the cone = 5cm.

(ii) h = l2r2(13)2(5)2

= 1692252=144 = 12cm.

Volume of the cone = 13πr2h=(13×π×5×5×12) cm3

= 100 πcm3.


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