Question

A semicircular lamina of radius 35cm is folded so that the two bounding radii are joined together to form a cone. Find the radius and the lateral surface area of the cone.

Answer 1

Length of the arc AB = theta/360 *2*pie*r

In case of semicircle theta=180°

Length of the arc AB= 180/360*2*pie*r = pie*r,

Where r =35cm

Length of the arc AB= 35 pie cm

Also the circumference of the base of cone will be equal to thelength of the arc. i.e., 2*pie*r = 35pie

r= 35/2 = 17 .5cm

C.S.A of the cone= pie*r*l where l is the slant height which will be equal to the radius of the original semi circular sheet.

i.e., C.S.A = pie*17.5*35

C.S.A = 1925 cm^2