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 cm
A cone is formed by folding it.
So the slant height of the cone, l = 35 cm
Let r1 be radius of cone.
Semicircular perimeter of lamina becomes the base of the cone.
r = 2r1
r = 2 r1
35 = 2 r1
r1 = 35/2= 17.5 cm
Hence the radius of the cone is 17.5 cm.
(ii) Curved surface area of the cone = r1l
= (22/7)×17.5×35
= 22×17.5×5
= 1925 cm2
Hence the lateral surface area of the cone is 1925 cm2.