a vessel in the shape of an inverted cone is surmounted by a cylinder has a common radius of 7 cm. it was filled with liquid till it covers one third of the height of the cylinder. if the height of each part is 9 cm and The vessel is turned upside down. find the volume of the liquid and what height will it reach in the cylindrical part.
Answers
964 cm³ is the volume of the liquid and upto 6 cm height cylinder will be filled
Step-by-step explanation:
Radius of cylinder = Radius of cone = 7 cm
Height of cone = Height of Cylinder = 9 cm
filled with liquid till it covers one third of the height of the cylinder.
=> height in cylinder = 9/3 = 3 cm
& Cone is filled completely
Volume of Liquid = Volume of cone + Volume of cylinder upto 3 cm height
= (1/3) π r² h + π r² h/3
= (1/3) (22/7) 7² * 9 + (22/7) 7² * 9/3
= 462 + 462
= 964 cm³
The vessel is turned upside down
Let say cylinder is filled till height h
=> π r² h = 964
=> (22/7) * 7² * h = 964
=> h = 6
upto 6 cm height cylinder will be filled
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volume of solid = 1/3 volume of cylinder +
volume of. cone
=>1/3πr²h+ 1/3πr²h
=>1/3*22/7*7*7*9+1/3*22/7*7*7*9
=>22/7 *7*3+ 22/7 *7*3
=>154*3+154*3
=>462+462
=>924 cm³