A sector is removed from a metallic disc and the remaining region is bent into the shape of a circular conical funnel with volume 2 3 . The least possible diameter of the disc is

Step-by-step solution

for a cone r will be cone slant height V=2 3 Let x radius of cone h be height then array l 1 3 r² h=2 3 x² h=6 3 x²= 6 3 h array least Diameter least slant height of cone ²= x ²+ h ² r ²= x ²+ h ² r²= 6 3 h +h² Diff. w. to x 2 r dr dh = -6 3 ~h ² +2 ~h for maximum & minimum dr dh =0 array l h = 3 h ²=3 x ²= 6 3 3 x ²=6 r ²=6+3 r ²=9 r =3 ~d =2 r d =6 array