The semicircle with the maximum possible radius is cut from a 14cm*7cm rectangular sheet of paper an

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16 May 2013 cone

The semicircle with the maximum possible radius is cut from a 14cm*7cm rectangular sheet of paper and cone is made out of it. Volume of the cone is

OPtion

1) 287/(32*sqrt3) cm^3
2) 395/(4*sqrt3) cm^3
3) 539/(32*sqrt3) cm^3
4) 539/(4*sqrt3) cm^3
5) 545/sqrt3 cm^3
6) 559/sqrt3 cm^3
7) 445/(2*sqrt3) cm^3
8) 565/sqrt2 cm^3
9) 565/(3*sqrt2)
10) None of these

Solution

Maximum possible radium = 7
Arc length of the semicircle = 22/7*7=22cm
let radius of cone = r
therefore 2*pi*r=22
r=7/2
height of the cone = h = sqrt(l^2-r^2) (where l=slant height)
using cone volume formula 1/3*pi*r^2*h=539/(4*sqrt3) cm^3
option 4

Correct Option: 4 Best Solution (0)