An Important Question of M.L Aggarwal book of class 10 Based on Mensuration Chapter for ICSE BOARD.

If a semi-circular lamina of a radius is folded so that the two bounding radii are joined together to form a cone. Find (i) the radius of the cone. (ii) the (lateral) surface area of the cone.

This is the Question Number 19, Exercise 17.2 of M.L Aggarwal.

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# A semi-circular lamina of radius 35 cm is folded so that the two bounding radii are joined together to form a cone. Find (i) the radius of the cone. (ii) the (lateral) surface area of the cone.

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(i)Given radius of the semi circular lamina, r = 35 cmA cone is formed by folding it.So the slant height of the cone,l= 35 cmLet r_{1}be radius of cone.Semicircular perimeter of lamina becomes the base of the cone.r = 2r_{1}r = 2

r_{1}35 = 2

r_{1}r_{1}= 35/2= 17.5 cmHence the radius of the cone is 17.5 cm.(ii) Curved surface area of the cone = r_{1}l= (22/7)×17.5×35= 22×17.5×5= 1925 cm

^{2}Hence the lateral surface area of the cone is 1925 cm

^{2}.