A hollow cylinder has solid hemisphere in one end and on the other end it is closed with a flat circular plate .The height of the water is 10 cm when flat circular surface is downward . Find the level of water , when it is inverted upside down , common diameter is 7cm and height of the cylinder is 20 cm . Explain with figure .
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Given
A hollow cylinder has a solid hemisphere inward at one end and on the other end, it id closed with a flat circular plate.
Height of the water when flat circular surface is downward (h)=10 cm
diameter (d)=7 cm
Height of the cylinder (h)=20 cm
Also, given to find the level of the water when it is inverted upside down.
[π=722]
Volume of water πr2h
=722×27×27×10
Volume of water =11×7×5
Volume of water =385 cm3 eq1
Now, to find the level opf the water when it is inverted upside down.
Now, the hemisphere will be down and water is inverted down
let the height of the water =h
[Volume = Volume of cylinder volume of hemisphere]
[∴ volume of cylinder =πr2h volume of hemisphere =32πr3 ]
v=π.r2.h−32.π.r3
π=722
V=722×27×27×h−32×722×27×27×27
V=977h−2×211×7×7⇔v=277h−277×37
[∵v=385] from eq (1)
V=277[h−37]⇔385=277[h−37]
⇒385×772=h−37⇔10=33h−7
30=3h−7⇔3h=30+7⇔h=337 cm
