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Question
Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
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Solution
Radius of hemispherical ends = radius of cylinder
`=1/2 xx 0.7`
`=7/20 m`
Total length = 2.7 m.
Height of cylinder
`=2.7 - 2 xx 7/20`
`= 2m`
Volume of two hemispheres
`=2 (2/3 pir^3)`
`=4/3 pir^3`
`=4/3 xx 22/7 xx (7/20)^3`
`=4/3 xx 22 /7 xx (343)/(800)`
` = 0.1797 m^3`
Volume of cylinders
` =pir^2h`
`=22/7 xx (7/20)^2 xx 2`
`=0.77 m^2`
Hence,
Volume of solid = 0.1797+0.77 = 0.95 m3
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