A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be `345\ c m^3`. Check whether she is correct, takin

Explanation

Radius of the spherical part , `R = (8.5 )/(2) cm `= 4.25 cm
Radius of the cylindrical neck , r = 1 cm .
Height of the cylindrical neck , h = 8 cm
Volume of the vessel ltbrge volume of the spherical part + volume of the cylindrical part
`4/3pi R^3 = pi r^2h = pi (4/3 R^3 - r^2 h)`
`=[3.14xx(4/3xx4.25 xx 4.25xx4.25 + 1 xx1xx8 )]cm^3`
`=[3.14 xx(102.354 + 8 )]cm^3`
`(3.14 xx 110. 354 ) cm^3 `
`=346.51156 cm^3 = 346.51 cm^3`
Hence , the volume found by Radhika is almost correct .